CBSE Questions for Class 10 Maths Quadratic Equations Quiz 6 - MCQExams.com

Find the roots of the following quadratic equations by using the quadratic formula
$$\displaystyle 2 \left( \frac{x}{x + 1} \right)^2 - 5 \left( \frac{x}{x + 1} \right) + 2 = 0, x \neq - 1$$
  • $$1, 2$$
  • $$1, -\cfrac{1}{2}$$
  • $$\cfrac{1}{2},-2$$
  • $$-2, 1$$
If  $$\displaystyle\alpha, \beta $$ are roots of $$\displaystyle ax^{2}-2bx+c=0$$ then $$\displaystyle a^{3}\beta ^{3}+a^{2}\beta ^{2}+a^{3}\beta^2$$ is
  • $$\displaystyle \frac{c^{2}\left ( c+2b \right )}{a^{3}}$$
  • $$\displaystyle \frac{bc^{2}}{a^{3}}$$
  • $$\displaystyle \frac{c^{2}}{a^{3}}$$
  • None
Solve $$9m^2-12m+2=0$$ by method of completing square.
  • $$\dfrac {2+\sqrt 2}{3}$$
  • $$\dfrac {\sqrt 2}{3}$$
  • $$2$$
  • $$\dfrac {-2+\sqrt 2}{3}$$
The roots of the equation $$\displaystyle x^{2}-px+q=0$$ are consecutive integers. Find the discriminate of the equation.
  • $$-1$$
  • $$0$$
  • $$1$$
  • None of these
Solve: $$\displaystyle x^{2}+3x+1=0 $$
  • $$\displaystyle x=\frac{3\pm\sqrt{5}}{2}$$
  • $$\displaystyle x=\frac{3+\sqrt{5}}{2},\frac{-3+\sqrt{5}}{2}$$
  • $$\displaystyle x=\frac{\pm{3}-\sqrt{5}}{2}$$
  • $$\displaystyle x=\frac{-3+\sqrt{5}}{2},\frac{-3-\sqrt{5}}{2}$$
Which of the statements given below is correct, if discriminant for equation  $$5x^2 - 4x +2 =0$$ is D ?
  • D > 0
  • D = 0
  • D < 0
  • D is not defined
Solve the equation using the quadratic formula
$$3{ x }^{ 2 }=-10x-5$$
  • $$\left\{ \displaystyle\frac { -5\pm \sqrt { 10 } }{ 3 } \right\} $$
  • $$\left\{ \displaystyle\frac { -10\pm \sqrt { 10 } }{ 3 } \right\} $$
  • $$\left\{ \displaystyle\frac { -10\pm \sqrt { 10 } }{ 6 } \right\} $$
  • $$\left\{ \displaystyle\frac { -5\pm \sqrt { 10 } }{ 6 } \right\} $$
The roots of the equation $$2{x}^{2}+x-4=0$$ are
  • $$1,-4$$
  • $$-3,\cfrac {1}{\sqrt {3}}$$
  • $$\cfrac{\sqrt {33}-1}{4},\cfrac{-\sqrt {33}-1}{4}$$
  • None
Solve the equation using the quadratic formula
$$2=-\displaystyle\frac { 10 }{ x } -\displaystyle\frac { 5 }{ { x }^{ 2 } } $$
  • $$\left\{ \displaystyle\frac { -5\pm \sqrt { 15 } }{ 2 } \right\} $$
  • $$\left\{ \displaystyle\frac { -5\pm \sqrt { 15 } }{ 4 } \right\} $$
  • $$\left\{ \displaystyle\frac { -5\pm \sqrt { 35 } }{ 2 } \right\} $$
  • $$\left\{ \displaystyle\frac { -10\pm \sqrt { 15 } }{ 2 } \right\} $$
When solved by the method of completing the square, the solutions to the equation $$ {-8x = 4x^{2}-1}$$ are 
  • $${\dfrac {-2+\sqrt{5}}{2}}$$
  • $${\dfrac {2+\sqrt{5}}{2}}$$
  • $${\dfrac {-2+\sqrt{2}}{2}}$$
  • $${\dfrac {-2-\sqrt{5}}{2}}$$
The roots of the equation $$(q -r)x^2+ (r -p)x + (p -q) =0$$ are
  • $$\dfrac {p-q}{q-r}, 1$$
  • $$\dfrac {q-r}{p-q}, 1$$
  • $$\dfrac {r-p}{p-q}, 1$$
  • $$\dfrac {r-p}{q-r}, 1$$
Find the number of real roots in the equation, $$\displaystyle { x }^{ 2 }+3x-9=0$$
  • $$1$$
  • $$2$$
  • $$0$$
  • None
Find the discriminant of $$\displaystyle { x }^{ 2 }-5x-10=0$$
  • $${65}$$
  • $${-65}$$
  • $$10$$
  • None of the above
Which of the following is not a quadratic equation
  • $$\displaystyle x-\frac { 3 }{ 2x } =5$$
  • $$\displaystyle 4x-\frac { 5 }{ 8 } ={ x }^{ 2 }$$
  • $$\displaystyle x+\frac { 1 }{ x } =9$$
  • $$\displaystyle 4x-\frac { 2 }{ 3x } =4{ x }^{ 2 }$$
Given that $${ z }^{ 2 }-10z+25=9$$, what is $$z$$?
  • $$ {3,4} $$
  • $$ {1,6} $$
  • $$ {2,6} $$
  • $$ {2,8} $$
If $$\displaystyle xy\neq 0$$ and $$\displaystyle { x }^{ 2 }{ y }^{ 2 }-xy=6$$, which of the following could be y in terms of x ?
I. $$\displaystyle \frac { 1 }{ 2x } $$
II. $$\displaystyle -\frac { 2 }{ x } $$
III. $$\displaystyle \frac { 3 }{ x } $$
  • I only
  • II only
  • I and II only
  • I and III only
  • II and III
Find the discriminant of $$\displaystyle pqr{ x }^{ 2 }-8pqx+pr=0$$
  • $$\displaystyle { p }^{ 2 }{ q }^{ 2 }-4{ p }^{ 2 }{ qr }^{ 2 }$$
  • $$\displaystyle 64{ p }^{ 2 }{ q }^{ 2 }-{ p }^{ 2 }{ r }^{ 2 }$$
  • $$\displaystyle 64{ p }^{ 2 }{ q }^{ 2 }-4{ p }^{ 2 }{ qr }^{ 2 }$$
  • $$\displaystyle 64{ p }^{ 2 }{ q }^{ 2 }-4{ p }^{ 2 }{ r }^{ 2 }$$
Find the number of real roots in the equation , $$\displaystyle 4{ x }^{ 2 }+3x+5=0$$
  • $$0$$
  • $$1$$
  • $$2$$
  • None
Which of the following is correct, if the roots of quadratic equation are equal?
  • $$\displaystyle D>0$$
  • $$\displaystyle D<0$$
  • $$\displaystyle D=0$$
  • None
The roots of the equation $$\displaystyle 2{ y }^{ 2 }+y-2=0$$ are
  • $$\displaystyle \frac { -1-\sqrt { 17 } }{ 2 } ,\frac { -1-\sqrt { 17 } }{ 2 } $$
  • $$\displaystyle \frac {- 1-\sqrt { 17 } }{ 4 } ,\frac { -1+\sqrt { 17 } }{ 4 } $$
  • $$\displaystyle -1-\sqrt { 17 } ,-1+\sqrt { 17 } $$
  • None
Which of the following equations are not quadratic?
  • $$x(2x+3)=x+2$$
  • $$(x-2)^2+1=2x-3$$
  • $$y(8y+5)=y^2+3$$
  • $$y(2y+15)=2(y^2+y+8)$$
Find the roots of equation by completing the square method:
$$\displaystyle 3{ x }^{ 2 }-12qx+12{ q }^{ 2 }=0$$
  • $$2q, 2q$$
  • $$-2q, -2q$$
  • $$-2q, 2q$$
  • None
Solve $$x^2+8x+15=0$$ by method of completing square.
  • $$x=3, -5$$
  • $$x=-3, -5$$
  • $$x=3, 5$$
  • $$x=-3, 5$$
If $$\alpha, \beta$$ are the roots of $$ax^2+bx+c=0$$ and $$\alpha +k, \beta +k$$ are the roots of $$px^2+qx+r=0$$, then $$\displaystyle\frac{b^2-4ac}{q^2-4pr}$$ is equal to:
  • $$\displaystyle\frac{a}{p}$$
  • $$1$$
  • $$\left(\displaystyle\frac{a}{p}\right)^2$$
  • $$0$$
Which of the following is correct if one root of quadratic equation is real?
  • $$\displaystyle D\le 0$$
  • $$\displaystyle D=0$$
  • $$\displaystyle D\ge 0$$
  • None
If a, b and c are real, then both the roots of the equation $$\left( x-b \right) \left( x-c \right) +\left( x-c \right) \left( x-a \right) +\left( x-a \right) \left( x-b \right) =0$$ are always
  • Positive
  • Negative
  • Real
  • Imaginary
Solve: $$p^2-12p+32=0$$
  • $$p=-8, 4$$
  • $$p=8, 4$$
  • $$p=8, -4$$
  • $$p=-8, -4$$
In the given equation, find the negative value of p.
$$\displaystyle p-3=\frac { 10 }{ p } $$
  • $$-2$$
  • $$-5$$
  • $$-10$$
  • None
Which of the following is a quadratic equation?
  • $$(a-1)x^{3}+(b -2)x^{2} + c$$
  • $$(a-1)x^{2}+(b -2)x + 5c$$
  • $$(a-1)x^{4}+(b -2)x^{2} + 2c$$
  • $$(x-1)x^{4}+(b -2)x^{2} + 2c$$
The solution of which of the following equations is same as that of $$40-6x=x^2$$?
  • $$y=(x-6)^2-40$$
  • $$y=(x-6)^2+40$$
  • $$y=(x+3)^2-49$$
  • $$y=(x+3)^2+49$$
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