Class10 Quiz Level 2 (Moderate) – Polynomials

Total questions: 20

Which of the following is an identify ?

Topic: Identifying polynomial

Deselect Answer

$ \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 $ \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

Deselect Answer

$ \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

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

Topic: Coefficient of a Roots

Deselect Answer

-8

None

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

Topic: Graphing polynomial

Deselect Answer

$ \displaystyle x=2$

$ \displaystyle x=4$

$\displaystyle x=-2$

$ \displaystyle x=1$

None

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

Topic: Differences of Squares

Deselect Answer

$ \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

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

Topic: Polynomial Substitution

Deselect Answer

None

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

Topic: Polynomial Substitution

Deselect Answer

None

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

Topic: Polynomial Functions

Deselect Answer

-1

None

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

Topic: Factorization

Deselect Answer

$ \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

10.

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

Topic: Nature of Roots

Deselect Answer

Real and distinct

Real and equal

Complex and distinct

No roots

None

11.

Which of the following is not an identify?

Topic: Polynomial Identity

Deselect Answer

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

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

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

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

None

12.

Factorize the polynomial $ \displaystyle {{x}^{4}}-25.$

Topic: Differences of Squares

Deselect Answer

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

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

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

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

None

13.

If $ \displaystyle p(x)=4{{x}^{2}}-7x+9,\text{ find }p=(-1).$

Topic: Polynomial Substitution

Deselect Answer

None

14.

If the sum of the roots of the polynomial $ \displaystyle {{x}^{2}}+4x+p$ is -3 and their product is 4, find tha value of $ \displaystyle p$.

Topic: Sum and Product of Roots

Deselect Answer

-4

-2

None

15.

Solve the quadratic equation $ \displaystyle {{x}^{2}}-7x+12=0.$

Topic: Solving Quadratics

Deselect Answer

3,4

4,3

2,5

1,12

None

16.

Factorize the polynomial $ \displaystyle 2{{x}^{2}}+5x+3.$

Topic: Factorization

Deselect Answer

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

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

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

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

None

17.

If the polynomial $ \displaystyle {{x}^{2}}+kx+25$ has equal roots, find tha value of $ \displaystyle k$.

Topic: Coefficients and Roots

Deselect Answer

None

18.

Factorize the polynomial $ \displaystyle {{x}^{2}}-14x+49$

Topic: Factorization

Deselect Answer

$ \displaystyle {{(x-7)}^{2}}$

$ \displaystyle {{(x+7)}^{2}}$

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

$ \displaystyle \left( {x+3} \right)\left( {x-16} \right)$

None

19.

The polynomial $ \displaystyle {{x}^{2}}+5x+6$ has roots:

Topic: Identifying Roots

Deselect Answer

-2,-3

2,3

3,-2

-3,2

None

20.

If the product of the roots of the polynomial $ \displaystyle {{x}^{2}}+px+q$ is 8 and their sum is -6, find the values of $ \displaystyle p\text{ and }q.$

Topic: Coefficients in Quadratics

Deselect Answer

$ \displaystyle p=6,q=8$

$ \displaystyle p=-6,q=8$

$ \displaystyle p=-6,q=-8$

$ \displaystyle p=6,q=-8$

None

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Class10 Quiz Level 2 (Moderate) – Polynomials

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