R d sharma solutions mathematics class 10 Solutions for Chapter 2 polynomials

Exercises in Chapter 2 polynomials Grade 10

Polynomials Exercise 2.1

Polynomials Exercise 2.2

Polynomials Exercise 2.3

Questions in Polynomials Exercise 2.1

Find the zeros of each of the following quadratic polynomials and verify the relationship between the zeros and their coefficients:

$\text { (i) } f(x)=x^{2}-2 x-8$

If α and β are the zeros of the quadratic polynomial f(x) = $x^{2}-5 x+4$ find the value of 1/α + 1/β

– 2αβ

If α and β are the zeros of the quadratic polynomial p(y) = $5 y^{2}-7 y+1$ find the value of 1/α+1/β.

If α and β are the zeros of the quadratic polynomial f(x)= $x^{2}-x-4$ find the value of 1/α+1/β–αβ

$\text { If one of the zero of the quadratic polynomial } f(x)=4 x^{2}-8 k x-9 \text { is negative of the other, then }$ find the value of k.

$\text { If the sum of the zeroes of the quadratic polynomial } f(t)=k t^{2}+2 t+3 k \text { is equal to their product, }$ then find the value of k.

$\text { If } \alpha \text { and } \beta \text { are the zeros of the quadratic polynomial } p(x)=4 x^{2}-5 x-1, \text { find the value of } a^{2} \beta+\alpha \beta^{2}$

$\text { If } \alpha \text { and } \beta \text { are the zeros of the quadratic polynomial } f(t)=t^{2}-4 t+3, \text { find the value of } \alpha^{4} \beta^{3}+\alpha^{3} \beta^{4} \text { . }$

Questions in Polynomials Exercise 2.2

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeros as 3, -1, and -3 respectively.

$\text { If the zeros of the polvnomial } f(x)=2 x^{3}-15 x^{2}+37 x-30 \text { are in A.P.. find them. }$

Questions in Polynomials Exercise 2.3

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm:

$\text { (i) } g(t)=t^{2}-3 ; f(t)=2 t^{4}+3 t^{3}-2 t^{2}-9 t-12$

$\text { (ii) } g(x)=x^{3}-3 x+1 ; f(x)=x^{5}-4 x^{3}+x^{2}+3 x+1$

$\text { (iii) } g(x)=2 x^{2}-x+3 ; f(x)=6 x^{5}-x^{4}+4 x^{3}-5 x^{2}-x-15$

$\text { Obtain all zeroes of the polynomial } \mathrm{f}(\mathrm{x})=2 \mathrm{x}^{4}+\mathrm{x}^{3}-14 \mathrm{x}^{2}-19 \mathrm{x}-6, \text { if two of its zeroes are }-2 \text { and }-1 .$

Obtain all zeroes of the polynomial $f(x)=x^{4}-3 x^{3}-x^{2}+9 x-6$ if the two of its zeroes are −√3

and √3

Obtain all zeroes of the polynomial $f(x)=2 x^{4}-2 x^{3}-7 x^{2}+3 x+6$ the two of its zeroes are −√(3/2) and √(3/2).

$\text { Find all the zeroes of the polynomial } x^{4}+x^{3}-34 x^{2}-4 x+120, \text { if the two of its zeros are } 2 \text { and }-2$