POLYNOMIALS

1. Find the value for K for which x4 + 10x3 + 25x2 + 15x + K exactly divisible by x + 7.

2. If two zeros of the polynomial f(x) = x4 - 6x3 - 26x2 + 138x – 35 are 2 3.Find the other zeros.

3. Find the Quadratic polynomial whose sum and product of zeros are 2 + 1, .

4. If , are the zeros of the polynomial 2x2 – 4x + 5 find the value of a) 2 + 2 b) ( - )2.

5. If , are the zeros of the polynomial x2 + 8x + 6 frame a Quadratic polynomial

whose zeros are a) and b) 1 + , 1 + .

6. On dividing the polynomial 4x4 - 5x3 - 39x2 - 46x – 2 by the polynomial g(x) the quotient is x2 - 3x – 5 and the remainder is -5x + 8.Find the polynomial g(x).

7. If , are the zeros of a Quadratic polynomial such that + = 24, - = 8. Find a Quadratic polynomial having and as its zeros.

9. Obtain all the zeros of the polynomial p(x) = 3x4 ─ 15x3 + 17x2 +5x ─6 if two

zeroes are ─1/√3 and 1/√3.

6

10.

11. Find the number of zeros of the polynomial from the graph given.

(Ans:1)

14. If one zero of the polynomial 3x2 - 8x +2k+1 is seven times the other, find the zeros and the value of k (Ans k= 2/3)

Self Practice

12. If (n-k) is a factor of the polynomials x2+px+q & x2 + m x+n. Prove that

k = n +

Ans : since (n – k) is a factor of x2 + px + q (n – k)2 + p(n- k) + q = 0And (n – k)2 + m(n – k) + n = 0

Solve this problem by yourself,

k = n +

SELF PRACTICE

16. If 2, ½ are the zeros of px2+5x+r, prove that p= r.17. If m, n are zeroes of ax2-5x+c, find the value of a and c if m + n = m.n=10

(Ans: a=1/2 ,c=5)18. What must be subtracted from 8x4 + 14x3 – 2x2 + 7x –8 so that the resulting

polynomial is exactly divisible by 4x2+3x-2. (Ans: 14x – 10)19. What must be added to the polynomial p(x)= x4 + 2x3 – 2x2 + x –1 so that the

resulting polynomial is exactly divisible by x2+2x-3. (Ans: x-2)

7