Class 10 Practice – Level 3 – Set 2- Quadratic Equations

Total questions: 15

If the quadratic equation $ \displaystyle 2{{x}^{2}}+kx+3=0$ has imaginary roots, which of the following must be true about $ \displaystyle k$?

Topic: Nature of Roots

$ \displaystyle \left| k \right|<4\sqrt{6}$

$ \displaystyle \left| k \right|>4\sqrt{6}$

$ \displaystyle \left| k \right|=4\sqrt{6}$

$ \displaystyle \left| k \right|=6$

None

Find the maximum value of the quadratic function $ \displaystyle y=-3{{x}^{2}}+12x-7.$

Topic: Maximum and Minimum Value

None

If one root of the quadratic equation $ \displaystyle 4{{x}^{2}}+9x+k=0$ is twice the other, what is the value of $ \displaystyle k$?

Topic: Roots of a Quadratic Equations

$ \displaystyle \dfrac{9}{{16}}$

$ \displaystyle \dfrac{9}{4}$

$ \displaystyle \dfrac{9}{8}$

$ \displaystyle \dfrac{9}{2}$

None

For what value of $ \displaystyle m$ does the quadratic equation $ \displaystyle {{m}^{2}}{{x}^{2}}+\left( {m+1} \right)x+1=0$ have real roots?

Topic: Discriminant and Nature of Roots

$ \displaystyle m\ge -2$

$ \displaystyle m>0$

$ \displaystyle m<0$

$ \displaystyle m\le -2$

None

Solve the quadratic equation $ \displaystyle 5{{x}^{2}}-13x+6=0$ using the quadratic formula. What are the roots?

Topic: Quadratic Formula Application

$ \displaystyle x=\dfrac{{13\pm \sqrt{{13}}}}{{10}}$

$ \displaystyle x=\dfrac{{13\pm \sqrt{{97}}}}{{10}}$

$ \displaystyle x=\dfrac{{13\pm \sqrt{{25}}}}{{10}}$

$ \displaystyle x=\dfrac{{13\pm \sqrt{{49}}}}{{10}}$

None

The vertex of the parabola $ \displaystyle y=3{{x}^{2}}-18x+27$ lies on which line?

Topic: Vertex of a Parabola

$ \displaystyle y=-9$

$ \displaystyle x=3$

$ \displaystyle y=9$

$ \displaystyle x=-3$

None

If the roots of the quadratic equation $\displaystyle a{{x}^{2}}+bx+c=0$ are in the ratio 1:2, find the condition that $ \displaystyle b\text{ and }c$ must satisfy.

Topic: Sum and product of Roots

$ \displaystyle 4ac={{b}^{2}}$

$ \displaystyle 4ac=b$

$ \displaystyle ac=2{{b}^{2}}$

$ \displaystyle {{b}^{2}}=2ac$

None

The quadratic equation $ \displaystyle {{x}^{2}}+px+q=0$ has real roots. What must be true about the discriminant?

Topic: Nature of Roots

Discriminant is positive

Discriminant is non-negative

Discriminant is negative

Discriminant is zero

None

If one root of the quadratic equation $ \displaystyle {{x}^{2}}-\left( {p+1} \right)x+p=0$ is 2, what is the value of $ \displaystyle p$?

Topic: Roots of a Quadratic Equations

None

10.

For what value of $ \displaystyle m$ does the quadratic equation $ \displaystyle {{x}^{2}}+mx+1=0$ have equal roots?

Topic: Quadratic Equations and Discriminant

$ \displaystyle m=2$

$ \displaystyle m=0$

$ \displaystyle m=-2$

$ \displaystyle m=-1$

None

11.

Determine the minimum value of the quadratic function $ \displaystyle y=2{{x}^{2}}-8x+7$.

Topic: Maximum and Minimum Value

-1

None

12.

Which of the following conditions must be satisfied for the quadratic equation $ \displaystyle a{{x}^{2}}+bx+c=0$ to have distinct roots?

Topic: Nature of Roots

$ \displaystyle {{b}^{2}}>4ac$

$ \displaystyle {{b}^{2}}\ge 4ac$

$ \displaystyle {{b}^{2}}=4ac$

$ \displaystyle {{b}^{2}}\le 4ac$

None

13.

Form a quadratic equation with roots $ \displaystyle \alpha =2$ and $ \displaystyle \beta =-3$ such that the coefficient of $ \displaystyle {{x}^{2}}$ is 2.

Topic: Quadratic Equations Formation

$ \displaystyle 2{{x}^{2}}+2x-6=0$

$ \displaystyle 2{{x}^{2}}-x-6=0$

$ \displaystyle 2{{x}^{2}}+x-6=0$

$ \displaystyle 2{{x}^{2}}-2x-6=0$

None

14.

Solve the quadratic equation $ \displaystyle 3{{x}^{2}}+2x-1=0$ using the quadratic formula. What are the roots?

Topic: Quadratic Formula Application

$ \displaystyle x=\dfrac{{-2\pm \sqrt{{16}}}}{6}$

$ \displaystyle x=\dfrac{{-2\pm \sqrt{8}}}{6}$

$ \displaystyle x=\dfrac{{2\pm \sqrt{8}}}{6}$

$ \displaystyle x=\dfrac{{2\pm \sqrt{{16}}}}{6}$

None

15.

If the roots of the quadratic equation $ \displaystyle a{{x}^{2}}+bx+c=0$ are in the ratio 2:3, find the value of $ \displaystyle {{b}^{2}}$ in terms of $ \displaystyle a\text{ and }c.$

Topic: Roots and Coefficients

$ \displaystyle {{b}^{2}}=10ac$

$ \displaystyle {{b}^{2}}=12ac$

$ \displaystyle {{b}^{2}}=8ac$

$ \displaystyle {{b}^{2}}=14ac$

None

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Class 10 Practice – Level 3 – Set 2- Quadratic Equations

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