Class 10 Practice – Level 2 – Set 1- Quadratic Equations

Total questions: 25

Solve the quadratic equation $ \displaystyle 3{{x}^{2}}-5x-2=0$ using the quadratic formula. what are the roots?

Topic: Solving Quadratic Equations

$ \displaystyle \frac{{5\pm \sqrt{{25+24}}}}{6}$

$\displaystyle \frac{{5\pm \sqrt{{25-24}}}}{6}$

$ \displaystyle \frac{{-5\pm \sqrt{{25+24}}}}{6}$

$ \displaystyle \frac{{-5\pm \sqrt{{25-24}}}}{6}$

None

For what value of k does the quadratic equation $ \displaystyle k{{x}^{2}}+4x+1=0$ have real and distinct roots?

Topic: Nature of Roots

k > 4

k < 4

k > 0

None

Find the maximum or minimum value of the quadratic function $ \displaystyle y=2{{x}^{2}}+8x-3$ .

Topic: Maximum and Minimum Value

Maximum value at y = 5

Minimum value at y = -5

Maximum value at y = -5

Minimum value at y = 5

None

If the roots of the quadratic equation $ \displaystyle {{x}^{2}}$ + p𝑥 + q =0 are real and equal , which of the following must be true?

Topic: Nature of Roots

$ \displaystyle {{p}^{2}}=4q$

$ \displaystyle {{p}^{2}}<4q$

$ \displaystyle {{p}^{2}}>4q$

$\displaystyle p=4q$

None

For which value of k will the quadratic equation $ \displaystyle {{x}^{2}}-2x+k=0$ have equal roots?

Topic: Discriminant

k = 1

k = 0

k = -1

k = 2

None

What is the y-coordinates of the vertex of the quadratic function $ \displaystyle y=3{{x}^{2}}-12x+7$ ?

Topic: Vertex of a Parabola

-4

-5

-3

None

If the sum of the roots of the quadratic equation $ \displaystyle a{{x}^{2}}+bx+c=0$ is 7 and the product of the roots is 12 , what are the values of b and c?

Topic: Sum and product of Roots

b = -7a, c = 12a

b = 7a, c = 12a

b = -7a, c = -12a

b = 7a, c =12 a

None

The discriminant of a quadratic equation is positive ,what can be inferred about the roots?

Topic: Nature of Roots

The roots are real and distinct

The roots are real and equal

The roots are real and imaginary

The roots are real equal

None

If one of the roots of the quadratic equation $ \displaystyle 4{{x}^{2}}-4x+1=0$ is 0.5, what is the other root?

Topic: Roots of a Quadratic Equations

0.5

-0.5

None

10.

The graph of $ \displaystyle y={{x}^{2}}+4x+k$ touches the x-axis at exactly one point. what is the value of k?

Topic: Graphs of Quadratic Functions

-4

None

11.

Form a quadratic equation with roots $ \displaystyle \alpha =2\text{ and }\beta =-3.$

Topic: Quadratic Equations Formation

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

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

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

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

None

12.

Solve the equation $\displaystyle 2{{x}^{2}}+7x+3=0$ using the quadratic formula.

Topic: Quadratic Formula Application

$ \displaystyle x=\frac{{-7\pm \sqrt{{25}}}}{4}$

$ \displaystyle x=\frac{{7\pm \sqrt{{25}}}}{4}$

$ \displaystyle x=\frac{{-7\pm \sqrt{{49}}}}{4}$

$ \displaystyle x=\frac{{7\pm \sqrt{{49}}}}{4}$

None

13.

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

Topic: Maximum and Minimum Value

-1

-3

None

14.

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

Topic: Nature of the Discriminant

Roots are equal and distinct

Roots are real and distinct

Roots are imaginary

Roots are equal

None

15.

The vertex of the parabola $ \displaystyle y={{x}^{2}}-6x+8$ lies on which axis?

Topic: Vertex and Axis of Symmetry

x-axis

y-axis

Line 𝑥 = 3

Line y = 8

None

16.

What is the product of the roots of the equation $ \displaystyle 4{{x}^{2}}-5x+1=0$ ?

Topic: Product of Roots

$ \displaystyle \frac{1}{4}$

$ \displaystyle -\frac{1}{4}$

None

17.

If the roots of the quadratic equation $\displaystyle 5{{x}^{2}}+13x+k=0$ are in the ratio 2:3 , what is the value of k?

Topic: Roots and Coefficients

None

18.

Factorize the quadratic expression $ \displaystyle 6{{x}^{2}}+11x-10$ .

Topic: Factorization

$\displaystyle \left( {3x+5} \right)\left( {2x-2} \right)$

$ \displaystyle \left( {3x-5} \right)\left( {2x+2} \right)$

$ \displaystyle \left( {3x+5} \right)\left( {2x-4} \right)$

$ \displaystyle \left( {3x-2} \right)\left( {2x+5} \right)$

None

19.

If the quadratic equation $ \displaystyle 2{{x}^{2}}+bx+3=0$ has onee root as $ \displaystyle \frac{1}{2}$ , what is the value of b?

Topic: Quadratic Equations and Roots

-2

-5

None

20.

Which of the following equations has real and distinct roots?

Topic: Real and Imaginary Roots

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

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

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

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

None

21.

Find the roots the equation $ \displaystyle 3{{x}^{2}}+7x-2=0$ using the quadratic formula?

Topic: Roots of a Quadratic Equations

$ \displaystyle x=\frac{{-7\pm \sqrt{{25}}}}{6}$

$ \displaystyle x=\frac{{-7\pm \sqrt{{49}}}}{6}$

$ \displaystyle x=\frac{{7\pm \sqrt{{25}}}}{6}$

$ \displaystyle x=\frac{{-7\pm \sqrt{{29}}}}{6}$

None

22.

What is the nature of the roots of the equation $ \displaystyle {{x}^{2}}+2x+2=0$ ?

Topic: Nature of Roots

Real and distinct

Real and equal

Imaginary

Undefined

None

23.

The vertex of the parabola $ \displaystyle y=3{{x}^{2}}+6x-2$ lies at:

Topic: Vertex of a Parabola

𝑥 = 1

𝑥 = -1

𝑥 = 2

𝑥 = -2

None

24.

The sum of the roots of the quadratic equation $ \displaystyle 2{{x}^{2}}+3x-5=0$ is ?

Topic: Sum of Roots

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

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

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

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

None

25.

The product of the roots quadratic equation $ \displaystyle 3{{x}^{2}}-4x+1=0$ is ;

Topic: Product of Roots

$ \displaystyle -\frac{1}{3}$

$ \displaystyle \frac{1}{3}$

-3

None

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Class 10 Practice – Level 2 – Set 1- Quadratic Equations

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