## 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}+2âˆš2x + 6

(v) q(x) = âˆš3x

^{2}+ 10x + 7âˆš3

(vi) f(x) = x

^{2}- (âˆš3+1)x + âˆš3

(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) -2âˆš3, -9

(iv) -3/2âˆš5, -1/2

**Solution**

3. If Î± and Î² are the zeros of the quadratic polynomial f(x) = x

^{2}â€“ 5x + 4, find the value of 1/Î± + 1/ Î² - 2 Î±Î².

**Solution**

4. If Î± and Î² are the zeros of the quadratic polynomial p(y) = 5y

^{2}- 7y + 1, find the value of 1/Î± + 1/Î² - 2Î±Î² .

**Solution**

5. If Î± and Î² are the zeros of the quadratic polynomial f(x) = x

^{2}- x - 4, find the value of 1/Î± + 1/ Î² - Î±Î² .

**Solution**

6. If Î± and Î² are the zeros of the quadratic polynomial f(x) = x

^{2}+ x - 2, find the value of 1/Î± - 1/ Î² .

**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 Î± and Î² are the zeros of the quadratic polynomial p(x) = 4x

^{2}- 5x - 1, find the value of Î±

^{2}Î² + Î±Î²

^{2}.

**Solution**

10. If Î± and Î² are the zeros of the quadratic polynomial f(t) = t

^{2}- 4t + 3 , find the value of Î±

^{4}Î²

^{3}+ Î±

^{3}Î²

^{4}.

**Solution**

11. If Î± and Î² are the zeros of the quadratic polynomial f(x) = 6x

^{2}+ x - 2 , find the value of Î±/Î² + Î²/Î±.

**Solution**

12. If Î± and Î² are the zeros of the quadratic polynomial p(s) = 3s

^{2}â€“ 6s + 4, find the value Î±/Î² + Î²/Î± + 2 (1/Î± + 1/Î²) + 3Î±Î² .

**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 Î± and Î² are the zeros of the quadratic polynomial f(x) = x

^{2}â€“ px + q , prove that Î±

^{2}/Î²

^{2}+ Î²

^{2}/ Î±

^{2}= p

^{4}/q

^{2}â€“ 4p

^{2}/q + 2

**Solution**

15. If Î± and Î² are the zeros of the quadratic polynomial f(x) = x

^{2}â€“ p(x+1) â€“ c, show that (Î± + 1) (Î²+1) = 1 â€“ c .

**Solution**

16. If Î± and Î² are the zeros of a quadratic polynomial such that Î± + Î² = 24 and Î± âˆ’ Î² = 8, find a quadratic polynomial have Î± and Î² as its zeros.

**Solution**

17. If Î± and Î² are the zeros of the quadratic polynomial f(x) = x

^{2}âˆ’ 1, find a quadratic polynomial whose zeroes are 2 Î±/Î² and 2 Î²/Î±

**Solution**

18. If Î± and Î² are the zeros of the quadratic polynomial f(x) = x

^{2}âˆ’ 3x âˆ’ 2, find a quadratic polynomial whose zeroes are 1/2Î± + Î² + 1/2Î² + Î± .

**Solution**

19. If Î± and Î² are the zeros of the polynomial f(x) = x

^{2}+ px + q , form a polynomial whose zeroes are (Î±+ Î²)

^{2}and (Î± â€“ Î²)

^{2}

**Solution**

20. If Î± and Î² are the zeros of the quadratic polynomial f(x) = x

^{2}â€“ 2x + 3, find a polynomial whose roots are (i) Î±+2, Î²+2 (ii) Î±â€“1/Î±+1, Î²â€“1/ Î²+1

**Solution**

21. If Î± and Î² are the zeros of the quadratic polynomial f(x) = ax

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

**Solution**