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

Total questions: 25

Solve the quadratic equation $\displaystyle {{x}^{2}}-4x-8=0$ using the quadratic formula . what are the roots ?

Topic: Solutions of Quadratic Equations

$ \displaystyle x=\frac{{4\pm \sqrt{{32}}}}{2}$

$ \displaystyle x=\frac{{-4\pm \sqrt{{32}}}}{2}$

$ \displaystyle x=\frac{{4\pm \sqrt{{48}}}}{2}$

$ \displaystyle x=\frac{{-4\pm \sqrt{{48}}}}{2}$

None

For what value of k does the quadratic equation $ \displaystyle 2{{x}^{2}}-kx+3=0$ have equal roots?

Topic: Nature of Roots

$ \displaystyle k=\sqrt{{24}}$

k = 24

$ \displaystyle k=2\sqrt{6}$

k = 12

None

What is the maximum value of the quadratic function $ \displaystyle y={{x}^{2}}+4x+1$ ?

Topic: Maximum and Minimum Value

None

If the discriminant of the quadratic equation is a perfect square, what can be said about the roots?

Topic: Discriminant

Roots are rational

Roots are irrational

Roots are imaginary

Roots are equal

None

If one of the roots of the quadratic equation $ \displaystyle {{x}^{2}}+7x+p=0$ is -3 , what is the value of p?

Topic: Roots of a Quadratic Equations

None

The graph of $ \displaystyle y=a{{x}^{2}}+bx+c$ passes though the point (1, 2) and the vertex is at (2, 3) what is the equation of the parabola if a = 1?

Topic: Graphs of Quadratic Functions

$ \displaystyle y={{x}^{2}}-4x+3$

$ \displaystyle y={{x}^{2}}-2x+3$

$ \displaystyle y={{x}^{2}}+2x+3$

$ \displaystyle y={{x}^{2}}-4x+6$

None

What is the x-coordinate of the vertex of the quadratic function $ \displaystyle y=2{{x}^{2}}-3x+1$?

Topic: Vertex of a Parabola

$ \displaystyle \dfrac{3}{4}$

$ \displaystyle -\dfrac{3}{4}$

$ \displaystyle \dfrac{3}{2}$

$ \displaystyle -\dfrac{3}{2}$

None

If the sum of the roots of a quadratic equation $ \displaystyle 3{{x}^{2}}+bx+c=0$ is 5 and the product of the roots is 2 ,what are the value of b and c?

Topic: Sum and product of Roots

$ \displaystyle b=-15,c=6$

$ \displaystyle b=-5,c=6$

$ \displaystyle b=-5,c=2$

$ \displaystyle b=-15,c=2$

None

The discriminant of the quadratic equation is zero. What can be inferred about the roots?

Topic: Nature of Roots

The roots are real and equal

The roots are real and distinct

The roots are imaginary

The roots are undefined

None

10.

If the quadratic equation $ \displaystyle 2{{x}^{2}}+px+2=0$ has one roots as $ \displaystyle \dfrac{1}{2}$ , what is the value of p?

Topic: Quadratic Equations and Roots

-3

-4

None

11.

Factorize the quadratic expression $ \displaystyle 3{{x}^{2}}+7x+2$ .

Topic: Factorization

$ \displaystyle \left( {3x+1} \right)\left( {x+2} \right)$

$ \displaystyle \left( {3x+2} \right)\left( {x+1} \right)$

$ \displaystyle \left( {3x-1} \right)\left( {x+2} \right)$

$ \displaystyle \left( {3x+1} \right)\left( {x+1} \right)$

None

12.

For which of the following values of k will be the quadratic equation $ \displaystyle {{x}^{2}}+kx+9=0$ have imaginary roots?

Topic: Discriminant and Nature of Roots

k = 4

k = -6

k = 6

k = =8

None

13.

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

Topic: Solving Quadratic Equations

3 and 2

6 and -1

1 and 6

-3 and 2

None

14.

What is the discriminant of the quadratic equation $ \displaystyle 4{{x}^{2}}+12x+9=0$ ?

Topic: Quadratic Equations and Discriminant

-1

None

15.

The quadratic equation $ \displaystyle 2{{x}^{2}}+4x+2=0$ has:

Topic: Nature of Roots

Two equal roots

Two distinct roots

Imaginary roots

No real roots

None

16.

Find the maximum value of the quadratic equation function $ \displaystyle y=2{{x}^{2}}-4x+1$ .

Topic: Maximum and Minimum Value

-1

-3

None

17.

The graph of the quadratic function $ \displaystyle y=2{{x}^{2}}-8x+6$ touches the x-axis at:

Topic: Graphs of Quadratic Functions

𝑥 = 2

𝑥 = 1

𝑥 = 3

𝑥 = 4

None

18.

Using the quadratic formula, solve $ \displaystyle 3{{x}^{2}}+5x-2=0$ , what are the roots?

Topic: Quadratic Formula Application

$ \displaystyle x=\dfrac{{-5\pm \sqrt{{49}}}}{6}$

$ \displaystyle x=\dfrac{{-5\pm \sqrt{{25}}}}{6}$

$\displaystyle x=\dfrac{{5\pm \sqrt{{25}}}}{6}$

$ \displaystyle x=\dfrac{{5\pm \sqrt{{49}}}}{6}$

None

19.

Find the real solutions to the system:

Topic: Solving Quadratic Equations

$ \displaystyle \begin{array}{l}{{x}^{2}}-{{y}^{2}}=4\\x+y=4.\end{array}$

(2.5,1.5)

(2,2)

(4,0)

(1.5,3)

None

20.

If one root of the equation $ \displaystyle {{x}^{2}}+7x+12=0$ is -3 , what is the other root?

Topic: Roots of a Quadratic Equations

-4

-2

None

21.

Which of the following quadratic equations has no real roots?

Topic: Nature of Roots

$ \displaystyle {{x}^{2}}+4x+5=0

$ \displaystyle {{x}^{2}}+2x+5=0

$ \displaystyle {{x}^{2}}+3x+5=0

$ \displaystyle {{x}^{2}}+4x+4=0

None

22.

The quadratic $\displaystyle {{x}^{2}}-6x+9=0$ has:

Topic: Nature of Roots

Real and distinct roots

Real and equal roots

Imaginary roots

Undefined roots

None

23.

Find the sum of the roots of equation $ \displaystyle 4{{x}^{2}}-10x+3=0$ .

Topic: Sum of Roots

$ \displaystyle \frac{5}{2}$

$ \displaystyle \frac{10}{4}$

$ \displaystyle -\frac{10}{4}$

$ \displaystyle -\frac{5}{2}$

None

24.

The product of the roots of the quadratic equation $ \displaystyle 2{{x}^{2}}-3x+1=0$ is :

Topic: Product of Roots

$ \displaystyle \dfrac{1}{2}$

$ \displaystyle \dfrac{3}{2}$

None

25.

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

Topic: Quadratic Formula Application

$ \displaystyle x=\dfrac{{-3\pm \sqrt{{17}}}}{4}$

$ \displaystyle x=\dfrac{{3\pm \sqrt{{17}}}}{4}$

$ \displaystyle x=\dfrac{{3\pm \sqrt{{13}}}}{4}$

$ \displaystyle x=\dfrac{{-3\pm \sqrt{{13}}}}{4}$

None

1 out of 25

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

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