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maths
Quadratic Equations
Solve the following quadratic equation...x2 + 3x + 2 = 0
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x = -1x = -2
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x = 1x = 2
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x = -1x = 2
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x = 1x = -2
Solve the following quadratic equation...x2 + 7x + 12 = 0
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x = -2x = -6
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x = -3x = -4
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x = -1x = -12
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x = 2x = 6
Solve the following quadratic equation...x2 + 9x + 20 = 0
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x = -2x = -10
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x = -5x = -4
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x = -1x = -20
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x = 4x = 5
Solve the following quadratic equation...x2 + 13x + 36= 0
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x = -2x = -18
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x = -9x = -4
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x = -3x = -12
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x = -6x = -6
Solve the following quadratic equation...x2 + 4x - 32 = 0
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x = 8x = -4
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x = -8x = 4
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x = -2x = 16
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x = 2x = -16
Solve the equation: 5x2 - 35x + 60 = 0
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x = 3, -4
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x = -3, 4
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x = 3, 4
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x = -3, -4
Solve the equation:4x2+2x - 6 = 0
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x = 1 & -1.5
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x = -1 & 1.5
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x = (-2 ±√92)/8
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x = (-2 ± √100)/8
What is the discriminant?
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b²-4ac
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b2/2a
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4ac
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b2±4ac
If the discriminant is negative, then the quadratic has:
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1 Real Solution
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2 Real Solutions
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Half a Solution
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No Real Solutions
If the discriminant equals 0, then the quadratic has:
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1 Real Solution
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2 Real Solutions
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Half a Solution
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No Real Solution
If the discriminant is positive, then the quadratic has:
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1 Real Solution
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2 Real Solutions
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Half a Solution
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No Real Solution
Use the quadratic formula to solve 2x2 + 2x - 12?
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-2, 3
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2, 3
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2, -3
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-2, -3
Solve using the quadratic formula...9x2 = 4 + 7x
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x = 2 and x = 3
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x = -1 and x = .25
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x = 1 and x = -.45
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x = 1.16, and x = -.38
If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the numbers.
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-9, 7
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√75
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9, -7
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15, -5
One leg of a right triangle is seven more than the other leg. The hypotenuse is eight more than the shorter leg. Find the lengths of the longest side.
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5 ft
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3 ft
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12 ft
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13 ft
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The graph of a quadratic function is called
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a line
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a hyperbola
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a parabola
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a cubic
Standard form of a quadratic equation
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y=x²
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y=ax²+bx+c
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y=mx+b
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y=x
What are the x- intercepts?
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x= 0 and x= -4
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x= 0 and x= 4
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y= 0
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x= 2
Does the equation open or or down? Y = -3x2 +7x - 2
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up
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down
The formula b2 - 4ac is called the
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quadratic formula
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factored form
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vertex formula
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the discriminant
If the discriminant is greater than zero, the equation has
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1 solution
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2 solutions
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no solutions
If the discriminant is less than zero, the equation has
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1 solution
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2 solutions
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no solutions
The equationy = x2 -12x + 36 has
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1 solution
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2 solutions
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no solutions
Find the roots of this equationx2 + x - 6 = 0
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4, -1
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3, -2
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-6, 1
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2, -3
What are the zeroes of this graph?
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x = -4 and 2
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x= -1 and 0
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x = 9 and -8
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x= 4 and -2
What is the factored quadratic equation in the following graph?
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y=(x+2)(x+6)
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y=x2-8x+12
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y=(x-2)(x-6)
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y=(x-4)(x+4)
Use the discriminant to find the number of solutions for the following equation.y = x2 +10x + 25
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2 solutions
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1 solution
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0 solutions
Does this graph have any roots?
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yes
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no
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I am not sure.
Say 'TRUE' or 'FALSE'A quadratic equation ax2 + bx + c = 0 has equal roots, then b2 - 4ac = 0
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TRUE
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FALSE
Say 'TRUE' or 'FALSE'Every Quadratic equation has exactly one root
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TRUE
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FALSE
The positive real root of the equation : 64x2 - 1 = 0 is ______
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8
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⅛
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1⁄16
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1⁄4
Can 0 be a root of a quadratic equation?
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Yes. Possible
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No. Not posssible
Is (x +1)2 = x2 + 2x + 1 is a quadratic equation?
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YES
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NO
Determine the values of a, b, and c for the quadratic equation: 4x2 – 8x = 3
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a = 4, b = -8, c = 3
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a = 4, b =-8, c =-3
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a = 4, b = 8, c = 3
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a = 4, b = 8, c = -3
What is a second degree polynomial equation?
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Linear Equations
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Quadratic Inequalities
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Quadratic Equations
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Quadratic Functions
What is the other term for quadratic equations?
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Equation of degree 3
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Equation of degree 0
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Equation of degree 2
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None of the above
What is the Latin word of quadratic?
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quadratum
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quadra
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quad
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None of the above
What is the meaning of the Latin word of quadratic?
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cube
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square
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Both a and b
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None of the above
Which of the following is an example of quadratic equations?
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x + 9 = 0
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x + y =12
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x3 + 5x2 - 14 =0
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x2 - 2x = 7
x - 12 = -x2 is an example of quadratic equation.
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True
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False
Which of the following is NOT an example of quadratic equations?
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2x2 - 3 = 2x
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-8x - 15 = -x2
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x + 3y = 45
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x2 + 7x + 10 = 0
What is the standard form of 9x - 16 = 3x - x2?
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x2 +12x -16 = 0
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2x2 + 9x -16 = 0
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x2 + 6x -16 = 0
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-x2 + 6x - 16= 0
Which of the following is in the standard form?
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y2 - 7y + 12 = 0
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x3 - x2 + 3x -8 = 0
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x2 +9x = 34
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y2 - 10 = -3y
What is another word for zeros?
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y-intercepts
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roots
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vertex
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axis of symmetry
Solve using the quadratic formula.2x2 - 9x - 35 = 0
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x = 7/2, x = -6
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x = -5/2, x =5
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x = -3/7, x =6
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x = -5/2, x = 7
If 12\frac{1}{2}21 is a root of the equation x2 + kx − 54x^2\ +\ kx\ -\ \frac{5}{4}x2 + kx − 45 then the value of k is
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2
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-2
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3
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-3
In the quadratic formula, if b2-4ac>0, then the quadratic equation has
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two imaginary solutions
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two different real solutions
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two equal real solutions
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none of these
The solution of the quadratic equation 4x2-5x-9=0 are
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x=-1 or x=9/4
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x=1 or x=9/4
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x=2 or x=3
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x=-2 or x=-3
In the expression 4x2-5x+9 the leading coefficient is
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9
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-5
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-4
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4
One solution of the quadratic equation x2-7x+12=0 is
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x=3
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x=2
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x=-3
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x=-2
Which of the followig trinomial is perfect square trinomial?
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x2+4x+9
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x2-22x-121
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x2+4x-9
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x2-22x+121
3x2 - 4 is a quadratic
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true
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false
The discriminant finds the
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number of solutions
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x-intercepts
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y-value of vertex
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y-intercept
The solutions of the quadratic equation x2-5x+6=0 are
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x=1 or x=-6
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x=3 or x=2
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x=-3 or x= 2
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x=-1 or x=6
If 3+2i is a solution of a quadratic equation, then other solution of this quadratic equation is
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2-3i
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3+2i
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1/3 -1/2i
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3-2i
True or false:The solution, root, x-intercept, and zero are all the same thing.
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True
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False, because the solution and root are the same but the x-intercept and zero are different
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False, because the x-intercept and root are the same but the zero and solution are different
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False, they are all different
Use the discriminant to find the number of solutions for the following equation.y = -3x2 +5x - 8
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2 solutions
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1 solution
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0 solutions
Use the discriminant to find the number of solutions for the following equation.y = 4x2 - 9
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2 solutions
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1 solution
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0 solutions
The non-zero root of the equation 3x - 5x2 = 0 is_____
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3⁄5
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5⁄3
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-3⁄5
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-5⁄3
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