## Chapter 2 Polynomials R.D. Sharma Solutions for Class 10th Math Exercise 2.1

**Exercise 2.1**

(i) f(x) = x

^{2}- 2x - 8

(ii) g(s) = 4s

^{2}- 4x + 1

(iii) h(t) = t

^{2}- 15

(iv) p(x) = x

^{2}+2√2x + 6

(v) q(x) = √3x

^{2}+ 10x + 7√3

(vi) f(x) = x

^{2}- (√3+1)x + √3

(vii) g(x) = a(x

^{2}+1) - x(a

^{2}+1)

(viii) 6x2 - 3 - 7x

**Solution**

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

(i) -8/3, 4/3

(ii) 21/8, 5/16

(iii) -2√3, -9

(iv) -3/2√5, -1/2

**Solution**

3. If α and β are the zeros of the quadratic polynomial f(x) = x

^{2}– 5x + 4, find the value of 1/α + 1/ β - 2 αβ.

**Solution**

4. If α and β are the zeros of the quadratic polynomial p(y) = 5y

^{2}- 7y + 1, find the value of 1/α + 1/β - 2αβ .

**Solution**

5. 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 .

**Solution**

6. If α and β are the zeros of the quadratic polynomial f(x) = x

^{2}+ x - 2, find the value of 1/α - 1/ β .

**Solution**

7. If one zeros of the quadratic polynomial f(x) = 4x

^{2}- 8kx - 9 is negative of the other , find the value of k .

**Solution**

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. product, find the value of k.

**Solution**

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**

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**

11. If α and β are the zeros of the quadratic polynomial f(x) = 6x

^{2}+ x - 2 , find the value of α/β + β/α.

**Solution**

12. If α and β are the zeros of the quadratic polynomial p(s) = 3s

^{2}– 6s + 4, find the value α/β + β/α + 2 (1/α + 1/β) + 3αβ .

**Solution**

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**

14. If α and β are the zeros of the quadratic polynomial f(x) = x

^{2}– px + q , prove that α

^{2}/β

^{2}+ β

^{2}/ α

^{2}= p

^{4}/q

^{2}– 4p

^{2}/q + 2

**Solution**

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**

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

**Solution**

17. If α and β are the zeros of the quadratic polynomial f(x) = x

^{2}− 1, find a quadratic polynomial whose zeroes are 2 α/β and 2 β/α

**Solution**

18. If α and β are the zeros of the quadratic polynomial f(x) = x

^{2}− 3x − 2, find a quadratic polynomial whose zeroes are 1/2α + β + 1/2β + α .

**Solution**

19. If α and β are the zeros of the polynomial f(x) = x

^{2}+ px + q , form a polynomial whose zeroes are (α+ β)

^{2}and (α – β)

^{2}

**Solution**

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) α–1/α+1, β–1/ β+1

**Solution**

21. If α and β are the zeros of the quadratic polynomial f(x) = ax

^{2}+ bx + c, the evaluate :-

**Solution**