## RD Sharma Class 10 Solutions Chapter 2 Polynomials

### RD Sharma Class 10 Solutions Polynomials Exercise 2.1

Question 1.

Find the zeros of each of the following quadratic polynomials and verify the relationship between the zeros and their co-efficients :

Solution:

(i) f(x) = x^{2} – 2x – 8

Question 2.

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.

Solution:

(i) Given that, sum of zeroes (S) = – \(\frac { 8 }{ 3 }\)

and product of zeroes (P) = \(\frac { 4 }{ 3 }\)

Required quadratic expression,

Question 3.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – 5x + 4, find the value of \(\frac { 1 }{ \alpha } +\frac { 1 }{ \beta } -2\alpha \beta\).

Solution:

Question 4.

If α and β are the zeros of the quadratic polynomial p(y) = 5y^{2} – 7y + 1, find the value of \(\frac { 1 }{ \alpha } +\frac { 1 }{ \beta }\)

Solution:

Question 5.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – x – 4, find the value of \(\frac { 1 }{ \alpha } +\frac { 1 }{ \beta } -\alpha \beta\)

Solution:

Question 6.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} + x – 2, find the value of \(\frac { 1 }{ \alpha } -\frac { 1 }{ \beta }\)

Solution:

Question 7.

If one zero of the quadratic polynomial f(x) = 4x^{2} – 8kx – 9 is negative of the other, find the value of k.

Solution:

Question 8.

If the sum of the zeros of the quadratic polynomial f(t) = kt^{2} + 2t + 3k is equal to their product, find the value of k.

Solution:

Question 9.

If α and β are the zeros of the quadratic polynomial p(x) = 4x^{2} – 5x – 1, find the value of α^{2}β + αβ^{2}.

Solution:

Question 10.

If α and β are the zeros of the quadratic polynomial f(t) = t^{2} – 4t + 3, find the value of α^{4}β^{3} + α^{3}β^{4}.

Solution:

Question 11.

If α and β are the zeros of the quadratic polynomial f (x) = 6x^{4} + x – 2, find the value of \(\frac { \alpha }{ \beta } +\frac { \beta }{ \alpha }\)

Solution:

Question 12.

If α and β are the zeros of the quadratic polynomial p(s) = 3s^{2} – 6s + 4, find the value of \(\frac { \alpha }{ \beta } +\frac { \beta }{ \alpha } +2\left( \frac { 1 }{ \alpha } +\frac { 1 }{ \beta } \right) +3\alpha \beta\)

Solution:

Question 13.

If the squared difference of the zeros of the quadratic polynomial f(x) = x^{2} + px + 45 is equal to 144, find the value of p

Solution:

Question 14.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – px + q, prove that:

Solution:

Question 15.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – p(x + 1) – c, show that (α + 1) (β + 1) = 1 – c.

Solution:

Question 16.

If α and β are the zeros of the quadratic polynomial such that α + β = 24 and α – β = 8, find a quadratic polynomial having α and β as its zeros.

Solution:

Question 17.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – 1, find a quadratic polynomial whose zeros are \(\frac { 2\alpha }{ \beta }\) and \(\frac { 2\beta }{ \alpha }\)

Solution:

Question 18.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – 3x – 2, find a quadratic polynomial whose zeros are \(\frac { 1 }{ 2\alpha +\beta }\) and \(\frac { 1 }{ 2\beta +\alpha }\)

Solution:

Question 19.

If α and β are the zeroes of the polynomial f(x) = x^{2} + px + q, form a polynomial whose zeros are (α + β)^{2} and (α – β)^{2}.

Solution:

Question 20.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – 2x + 3, find a polynomial whose roots are :

(i) α + 2, β + 2

(ii) \(\frac { \alpha -1 }{ \alpha +1 } ,\frac { \beta -1 }{ \beta +1 }\)

Solution:

Question 21.

If α and β are the zeros of the quadratic polynomial f(x) = ax^{2} + bx + c, then evaluate :

Solution:

RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.1

### RD Sharma Class 10th Solutions Chapter 2 Polynomials Ex 2.2