Class 10 Practice – Level 2 – Set 1 – Polynomials

Total questions: 25

If $ \displaystyle \alpha \text{ and }\beta $ are the zeros of the polynomial $ \displaystyle {{x}^{2}}-5x+6$ , what is the value of $ \displaystyle \alpha \text{ + }\beta \text{ and }\alpha \text{ }\text{. }\beta $?

Topic: Relationship between zeros and Coefficients

$ \displaystyle \alpha \text{ + }\beta =5,\alpha \text{ }\text{. }\beta =6$

$ \displaystyle \alpha \text{ + }\beta =6,\alpha \text{ }\text{. }\beta =5$

$\displaystyle \alpha \text{ + }\beta =8,\alpha \text{ }\text{. }\beta =6$

$ \displaystyle \alpha \text{ + }\beta =9,\alpha \text{ }\text{. }\beta =4$

None

Factorize the polynomial $ \displaystyle {{x}^{3}}-3{{x}^{2}}-4x+12$ .

Topic: Factorization

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

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

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

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

None

Find the zeros of the polynomial $ \displaystyle 2{{x}^{2}}-8x+6$ .

Topic: Zeros of polynomial

1, 3

-1, 3

-2, -3

3, 1

None

Which of the following is an identify ?

Topic: Identifying polynomial

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

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

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

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

None

If one root of the polynomial $ \displaystyle {{x}^{2}}-7x+10$, If one root is 5, then find the other root?

Topic: Polynomial Roots

None

What is the quotient when the polynomial $\displaystyle 2{{x}^{3}}-9{{x}^{2}}+4x+15$ is divided by x - 3?

Topic: Synthetic division

$ \displaystyle 2{{x}^{2}}-3x-5$

$ \displaystyle 2{{x}^{2}}-3x+5$

$ \displaystyle 2{{x}^{2}}-5x-5$

$ \displaystyle 2{{x}^{2}}-5x+5$

None

If the polynomial $ \displaystyle {{x}^{2}}+4x+k$ has roots 2 and -2 , what is the value of k?

Topic: Coefficient of a Roots

-8

None

Factorize the polynomial $ \displaystyle 3{{x}^{3}}-3{{x}^{2}}+4x-4$ .

Topic: Factoring by Grouping

$ \displaystyle \left( {3{{x}^{2}}+4} \right)\left( {x-1} \right)$

$ \displaystyle \left( {3x+4} \right)\left( {{{x}^{2}}-1} \right)$

$ \displaystyle \left( {{{x}^{2}}+4} \right)\left( {3x-1} \right)$

$ \displaystyle \left( {3x-4} \right)\left( {{{x}^{2}}+1} \right)$

None

The graph of the polynomial $ \displaystyle y={{x}^{2}}-4x+4$ touches the x axis at :

Topic: Graphing polynomial

$ \displaystyle x=2$

$ \displaystyle x=4$

$\displaystyle x=-2$

$ \displaystyle x=1$

None

10.

If the sum of the roots of the polynomial $ \displaystyle {{x}^{2}}+px+q$ is - 5 and their product is 6 , find the values of p and q .

Topic: Coefficients in Quadratics

p = 5, q = 6

p = -5, q = 6

p = -5, q = -6

p = 5, q = -6

None

11.

If $ \displaystyle p\left( x \right)={{x}^{2}}-3x+4$ , find p(2.)

Topic: Polynomial Substitution

None

12.

If the sum of the roots of the polynomial $ \displaystyle {{x}^{2}}+7x+10$ is - 7, what is the product of the roots?

Topic: Sum and Product of Roots

-10

-7

None

13.

Divide the polynomial $ \displaystyle 2{{x}^{3}}+3{{x}^{2}}-5x+6\text{ by }x-2$ and find the remainder.

Topic: Polynomial Division

None

14.

Determine the nature of the roots of the polynomial $ \displaystyle {{x}^{2}}+4x+5$ .

Topic: Nature of Roots

Real and distinct

Real and equal

Complex and distinct

No roots

None

15.

Solve the quadratic equation $\displaystyle {{x}^{2}}-8x+15=0$ .

Topic: Solving Quadratics

3, 5

5, 3

2, 8

1, 15

None

16.

For the polynomial $ \displaystyle f\left( x \right)=2{{x}^{3}}-{{x}^{2}}+3x-5$ , find f( - 1).

Topic: Polynomial Functions

-11

-7

-5

None

17.

Factorize the polynomial $ \displaystyle x{}^{4}-16$ .

Topic: Differences of Squares

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

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

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

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

None

18.

The polynomial $\displaystyle {{x}^{2}}+3x-4$ has roots:

Topic: Identifying Roots

4, -1

-4, 1

2, -2

3, -4

None

19.

For the polynomial $ \displaystyle g\left( x \right)={{x}^{3}}-2{{x}^{2}}+x-2\text{ find }g\left( 2 \right).$

Topic: Polynomial Functions

-1

None

20.

The discriminant of the polynomial $ \displaystyle {{x}^{2}}-6x+9$ is:

Topic: Discriminant Roots

-9

None

21.

If $ \displaystyle p\left( x \right)=3{{x}^{2}}-4x+5$ ,find p (- 2).

Topic: Polynomial Substitution

None

22.

For the polynomial $ \displaystyle 2{{x}^{2}}-5x+3$ , what is the sum of the roots?

Topic: Sum of Roots

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

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

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

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

None

23.

Determine the nature of the roots of the polynomial $ \displaystyle {{x}^{2}}+2x+5$?

Topic: Nature of Roots

Real and distinct

Real and equal

Complex and distinct

No roots

None

24.

Factorize the polynomial $ \displaystyle {{x}^{2}}-10x+25$ .

Topic: Factorization

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

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

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

$ \displaystyle \left( {x+3} \right)\left( {x-7} \right)$

None

25.

If one root of the cubic polynomial $ \displaystyle {{x}^{3}}-6{{x}^{2}}+11x-6$ is 1 , what are the other roots?

Topic: Cubic polynomial

2, 3

3, 2

4, 5

1, 2

None

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Class 10 Practice – Level 2 – Set 1 – Polynomials

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