CBSE Questions for Class 10 Maths Quadratic Equations Quiz 1 - MCQExams.com

Solve the following equations.
$$x^4\,-\,3x^2\,+\,2\,=\,0$$, roots are 

  • $$x\,=\,\pm\,\sqrt3,\,\pm\,1$$
  • $$x\,=\,\pm\,\sqrt2,\,\pm\,1$$
  • $$x\,=\,\pm\,\sqrt2,\,\pm\,3$$
  • none of the above
Which of the following methods is used to derive the Standard Quadratic Formula for the Quadratic Equation $$ax^2+bx+c=0$$?
  • Factorisation Method
  • Completing Square Method
  • Hit and Trial Method
  • All the above.
Let $$\alpha(a)$$ and $$\beta(a)$$ be the roots of the equation $$\\ \left( \sqrt [ 3 ]{ 1+a } -1 \right) x^{ 2 }+\left( \sqrt { 1+a } -1 \right) x+\left( \sqrt [ 6 ]{ 1+a } -1 \right) =0$$
$$\displaystyle \lim _{ a\rightarrow 0 }{ \alpha  } \left( a \right)$$ and $$\displaystyle \lim _{ a\rightarrow 0 }{ \beta  } \left( a \right)$$ are
  • $$-\dfrac{5}{2}$$ and $$1$$
  • $$-\dfrac{11}{2}$$ and $$-1$$
  • $$-\dfrac{7}{2}$$ and $$2$$
  • $$-\dfrac{9}{2}$$ and $$3$$
The roots of the equation $$\sqrt{3y + 1} = \sqrt{y - 1}$$  are?
  • $$- 1$$
  • $$2, 3$$
  • $$2, 1$$
  • None of these
A quadratic equation in $$x$$ is $$ax^2 + bx + c = 0$$, where $$a, b, c$$ are real numbers and the other condition is
  • $$a \neq 0$$
  • $$b \neq 0$$
  • $$c \neq 0$$
  • $$b = 0$$
Find the roots of following quadratic equation 
$$x^2\,+\,3x\,-\,2\,=\,0$$
  • $$\displaystyle\,x\,=\,\frac{-3\,\pm\,\sqrt{15}}{2}$$
  • $$\displaystyle\,x\,=\,\frac{-3\,\pm\,\sqrt{17}}{2}$$
  • $$\displaystyle\,x\,=\,\frac{-3\,\pm\,\sqrt{19}}{2}$$
  • $$\displaystyle\,x\,=\,\frac{-3\,\pm\,\sqrt{21}}{2}$$
Find the discriminant for the given quadratic equation:
$$\sqrt{3}x^2\,+\,2\sqrt{2}x\,-\,2\sqrt{3}\,=\,0$$
  • $$26$$
  • $$32$$
  • $$38$$
  • $$44$$
Find the discriminant for the given equation:
$$3x^2\,+\,2x\,-\,1\,=\,0$$
  • $$11$$
  • $$13$$
  • $$15$$
  • $$16$$
Find the discriminant for the given quadratic equation: $$x^2\,+\,4x\,+\,k\,=\,0$$
  • $$6\,-\,4k$$
  • $$16\,-\,4k$$
  • $$16\,-\,3k$$
  • $$13\,-\,2k$$
Find the value of discriminant for the following equation.
$$x^{2}\, +\, 4x\, +\, k\, =\, 0$$
  • $$\Delta\, =\, 16\, + 4k$$
  • $$\Delta\, =\, 16\, -4k$$
  • $$\Delta\, =\, 16\, - k$$
  • $$\Delta\, =\, 16+k$$
Say true or false.
A quadratic equation cannot be solved by the method of completing the square.
  • True
  • False
The discriminant of $$ax^{2}-(a+b)x+b=0$$ is:
  • $$a-b$$
  • $$a+b$$
  • $$(a+b)^{2}$$
  • $$(a-b)^{2}$$
If a given expression is a complete square, then which of the following formulae we use to factorize it?
  • $$a^2 + 2ab+b^2=(a+b)^2$$
  • $$a^2 - 2ab+b^2=(a-b)^2$$
  • $$(a - b) (a + b) = (a^2 -b^2)$$
  • $$(x+a)(x+b)=x^2+(a+b)x+ab$$
For the expression $$ax^2 + 7x + 2$$ to be quadratic, the necessary condition is
  • $$a=0$$
  • $$a \neq 0$$
  • $$ a> \cfrac{7}{2}$$
  • $$ a<-1 $$
Find the value of discriminant for the following equation.
$$2x^{2}\, +\, x\, +\, 1\, =\, 0$$
  • $$7$$
  • $$-7$$
  • $$9$$
  • $$-9$$
The discriminant (D) of $$\sqrt{x^{2}+x+1}=2$$ is:
  • -3
  • 13
  • 11
  • 12
If the discriminant of $$3x^{2}-14x+k=0$$ is $$100$$, then $$k=$$
  • $$8$$
  • $$32$$
  • $$16$$
  • $$24$$
Which of the following is a quadratic polynomial in one variable?
  • $$\sqrt{2x^{3}}+5$$
  • $$2x^2 + 2x^{-2}$$
  • $$x^2$$
  • $$2x^2+y^2$$
The mentioned equation is in which form?
$$3y^{2}\,-\, 7\, =\, \sqrt{3}\,y$$
  • linear
  • Quadratic
  • Cubic
  • None
Which of the following is a quadratic equation ?
  • $$x^{\frac{1}{2}}+2x+3=0$$
  • $$(x^2-1)(x+4)=x^{2}+1$$
  • $$x^{2}-3x+5=0$$
  • $$(2x^2+1)(3x-4)=6x^{2}+3$$
The condition for $$px^{2}+qx+r=0$$ to be pure quadratic is:
  • $$p=0$$
  • $$q=0$$
  • $$r=0$$
  • $$p=q=0$$
The mentioned equation is in which form?
$$\cfrac {3}{4}y^{2}\, =\, 2y\, +\,7$$
  • cubic
  • quadratic
  • linear
  • none of these
The mentioned equation is in which form?
$$(y\, -\, 2)\, (y\, +\, 2)\, =\, 0$$
  • cubic
  • quadratic
  • linear
  • none of these
The mentioned equation is in which form?
$$m^{3}\, +\, m\, +\, 2\, =\, 4m$$
  • Linear
  • Quadratic
  • Quartic
  • None
The mentioned equation is in which form?
$$y^{2}\, -\, 4\, =\, 11y$$
  • Quadratic
  • linear
  • Cubic
  • None
The mentioned equation is in which form?
$$z\, -\, \cfrac{7}{z}\, =\, 4z\, +\, 5$$
  • Linear
  • Quadratic
  • cubic
  • None of these
The mentioned equation is in which form?
$$n\, -\, 3\, =\, 4n$$
  • linear
  • Quadratic
  • constant
  • None
STATEMENT - 1 : $$(x-2)(x+1)$$ $$=$$ $$(x-1)(x+3)$$ is a quadratic equation.
STATEMENT - 2 : If $$p(x)$$ is a quadratic polynomial, then $$p(x)$$ $$=$$ $$0$$ is called a quadratic equation.
  • Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1
  • Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1
  • Statement - 1 is True, Statement - 2 is False
  • Statement - 1 is False, Statement - 2 is True
Is the following equation quadratic?
$$(x\, +\, 3) (x\, -\, 4)\, =\, 0$$
  • Yes
  • No
  • Ambiguous
  • Data insufficient
Is the following equation quadratic?
$$n^{3}\, -\, n\, +\, 4\, =\, n^{3}$$
  • Yes
  • No
  • Ambiguous
  • Data insufficient
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