Class 10 Practice – Level 1 – Quadratic Equations

Total questions: 40

What is the standard form of a quadratic equation?

Topic: Basic Concepts of Quadratic Equations

$ \displaystyle a{{x}^{2}}+bx+c=0$

$ \displaystyle ax+b=0$

$ \displaystyle a{{x}^{2}}+bx=0$

$ \displaystyle a{{x}^{2}}=0$

None

If one of the roots of the quadratic equation $ \displaystyle {{x}^{2}}-5x+6=0$ is 2, what is the other root?

Topic: Solutions of Quadratic Equations

None

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

Topic: Discriminant

-2

None

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

Topic: Nature of Roots

Roots are real and equal

Roots are real and distinct

Roots are imaginary

Roots are zero

None

What is the quadratic formula used to find the roots of a quadratic equation $ \displaystyle a{{x}^{2}}+bx+c=0?$

Topic: Quadratic Formula

$ \displaystyle \frac{{-b\pm \sqrt{{{{b}^{2}}-4ac}}}}{{2a}}$

$ \displaystyle \frac{{-b\pm \sqrt{{{{b}^{2}}+4ac}}}}{{2a}}$

$ \displaystyle \frac{{-b\pm \sqrt{{4ac-{{b}^{2}}}}}}{{2a}}$

$ \displaystyle \frac{{-b+\sqrt{{{{b}^{2}}-4ac}}}}{{2a}}$

None

Solve the quadratic equation $ \displaystyle {{x}^{2}}-7x+12=0$ by factorization. What are the roots?

Topic: Solving Quadratic Equations

4 and 3

6 and 2

5 and 2

4 and 2

None

If the roots of the quadratic equation $ \displaystyle {{x}^{2}}-4x+k=0$ are equal, what is the value of $\displaystyle k$?

Topic: Roots and Coefficients

None

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

Topic: Nature of the Discriminant

Roots are real and equal

Roots are real and distinct

Roots are imaginary

Roots are undefined

None

What is the sum of the roots of the quadratic equation $ \displaystyle {{x}^{2}}+6x+8=0?$

Topic: Roots and Sum/Product

-6

-8

None

10.

Which of the following quadratic equations has real and distinct roots?

Topic: Discriminant and Nature of Roots

$ \displaystyle {{x}^{2}}+2x+1=0$

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

$ \displaystyle {{x}^{2}}+x+1=0$

$ \displaystyle {{x}^{2}}-5x+6=0$

None

11.

What are the roots of the quadratic equation $ \displaystyle {{x}^{2}}+3x-10=0?$

Topic: Solving Quadratic Equations

5 and -2

-5 and 2

2 and -5

-5 and -2

None

12.

The graph of the quadratic formula $ \displaystyle y=a{{x}^{2}}+bx+c$ is a parabola. Which direction does it open if $ \displaystyle a>0?$

Topic: Graphs of Quadratic Functions

Upwards

Downwards

Leftwards

Rightwards

None

13.

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

Topic: Vertex of a Parabola

-1

None

14.

If the roots of the quadratic equation $ \displaystyle {{x}^{2}}-9x+20=0$ are $ \displaystyle \alpha $ and $ \displaystyle \beta $, what is the sum of the roots?

Topic: Sum of Roots

-9

-20

None

15.

For the quadratic equation $\displaystyle 3{{x}^{2}}-5x+2=0$, what is the product of the roots?

Topic: Product of Roots

$ \displaystyle \frac{2}{3}$

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

$ \displaystyle -2$

None

16.

Factorize the quadratic expression $ \displaystyle {{x}^{2}}-4x-12.$

Topic: Factorization

$ \displaystyle \left( {x-6} \right)\left( {x+2} \right)$

$ \displaystyle \left( {x-4} \right)\left( {x+3} \right)$

$ \displaystyle \left( {x-6} \right)\left( {x-2} \right)$

$ \displaystyle \left( {x-3} \right)\left( {x+4} \right)$

None

17.

Form a quadratic equation with roots 3 and -4.

Topic: Quadratic Equations Formation

$ \displaystyle {{x}^{2}}+x-12=0$

$ \displaystyle {{x}^{2}}-x-12=0$

$ \displaystyle {{x}^{2}}+x+12=0$

$ \displaystyle {{x}^{2}}-x+12=0$

None

18.

In the quadratic equation $ \displaystyle 2{{x}^{2}}+bx+8=0,$ the sum of the roots is -4, What is the value of $ \displaystyle b$?

Topic: Coefficient and Roots

-8

-4

None

19.

Which quadratic equation has equal roots?

Topic: Nature of Roots

$ \displaystyle {{x}^{2}}-2x+1=0$

$ \displaystyle {{x}^{2}}-4x+3=0$

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

$ \displaystyle {{x}^{2}}-5x+6=0$

None

20.

The quadratic equation $ \displaystyle {{x}^{2}}+10x+25=0$ is a perfect square. What is its factorization?

Topic: Factoring Quadratics

$ \displaystyle {{\left( {x+5} \right)}^{2}}$

$ \displaystyle {{\left( {x-5} \right)}^{2}}$

$ \displaystyle {{\left( {x+10} \right)}^{2}}$

$ \displaystyle {{\left( {x-10} \right)}^{2}}$

None

21.

If $ \displaystyle x=-2$ is a root of the quadratic equation $ \displaystyle {{x}^{2}}+px-6=0,$ find the value of $ \displaystyle p$.

Topic: Quadratic Equations and Roots

None

22.

The roots of the quadratic equation $ \displaystyle {{x}^{2}}-7x+10=0$ are:

Topic: Roots of a Quadratic Equations

5 and 2

-5 and -2

3 and 4

1 and 10

None

23.

Simplify the quadratic expression $ \displaystyle {{x}^{2}}+6x+9.$

Topic: Simplifying Quadratics

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

$ \displaystyle {{\left( {x+9} \right)}^{2}}$

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

$ \displaystyle {{\left( {x-9} \right)}^{2}}$

None

24.

What is the vertex form of the quadratic equation $ \displaystyle y={{x}^{2}}+4x+4?$

Topic: Graphical Representation

$ \displaystyle y={{\left( {x+2} \right)}^{2}}$

$ \displaystyle y={{\left( {x-2} \right)}^{2}}$

$ \displaystyle y={{\left( {x+4} \right)}^{2}}$

$ \displaystyle y={{\left( {x-4} \right)}^{2}}$

None

25.

Find the quadratic equation whose roots are 3 and 5.

Topic: Sum and product of Roots

$ \displaystyle {{x}^{2}}-8x+15=0$

$ \displaystyle {{x}^{2}}-2x+15=0$

$ \displaystyle {{x}^{2}}-6x+15=0$

$ \displaystyle {{x}^{2}}-8x+6=0$

None

26.

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

Topic: Quadratic Formula Application

1 and -2.5

-1 and 2.5

5 and -1

2 and -0.5

None

27.

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

Topic: Roots and Discriminant

-1

None

28.

The minimum value of the quadratic function $ \displaystyle y={{x}^{2}}-4x+5$ occurs at:

Topic: Maximum and Minimum Value

$ \displaystyle x=2$

$ \displaystyle x=-2$

$ \displaystyle x=0$

$ \displaystyle x=4$

None

29.

The quadratic function $ \displaystyle y={{x}^{2}}-6x+9$ represents a parabola. What is the vertex of this parabola?

Topic: Graphical Representation

(3,0)

(0,3)

(2,1)

(1,2)

None

30.

Which of the following quadratic equations has real and distinct roots?

Topic: Real and Distinct Roots

$ \displaystyle {{x}^{2}}-4x+3=0$

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

$ \displaystyle {{x}^{2}}+2x+1=0$

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

None

31.

Which of the following expressions completes the square for $ \displaystyle {{x}^{2}}+10x?$

Topic: Completing the Square

$ \displaystyle {{\left( {x+5} \right)}^{2}}-25$

$ \displaystyle {{\left( {x+5} \right)}^{2}}+25$

$ \displaystyle {{\left( {x-5} \right)}^{2}}+25$

$ \displaystyle {{\left( {x-5} \right)}^{2}}-25$

None

32.

Find the value of $ \displaystyle k$ if $ \displaystyle x=2$ is a root of the equation $ \displaystyle 3{{x}^{2}}+kx-8=0$.

Topic: Coefficient and Roots

-1

-2

None

33.

Which value of $ \displaystyle k$ will make the quadratic equation $ \displaystyle 4{{x}^{2}}+kx+1=0$ have equal roots?

Topic: Quadratic Equations Formation

-4

-2

None

34.

The quadratic equation $ \displaystyle {{x}^{2}}+8x+16=0$ has:

Topic: Nature of Roots

Two equal roots

Two distinct roots

No real roots

One real root

None

35.

The quadratic equation $ \displaystyle {{x}^{2}}+2x+5=0$ has:

Topic: Real and Imaginary Roots

Real and distinct roots

Equal roots

Imaginary roots

Undefined roots

None

36.

The sum of the roots of $ \displaystyle {{x}^{2}}-3x+2=0$ is:

Topic: Sum of Roots

-2

-3

None

37.

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

Topic: Product of Roots

$ \displaystyle \frac{1}{2}$

$ \displaystyle \frac{3}{2}$

None

38.

For the quadratic equation $ \displaystyle 5{{x}^{2}}+9x+4=0$, what is the sum of the roots?

Topic: Quadratic Roots

-9

-5

None

39.

Which of the following quadratic equations has no real roots?

Topic: Nature of Roots

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

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

$ \displaystyle {{x}^{2}}-2x+1=0$

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

None

40.

Which of the following expressions is a quadratic equation?

Topic: Solving Quadratic Equations

$ \displaystyle 3{{x}^{2}}+7x+1=0$

$ \displaystyle 4x+2=0$

$ \displaystyle 5x-9=0$

$ \displaystyle 7{{x}^{3}}+4{{x}^{2}}=0$

None

1 out of 40

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Class 10 Practice – Level 1 – Quadratic Equations

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