Chapter 2 Polynomials)
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POLYNOMIALS1.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, 1 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)
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.
b) 1 +
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 nq k=n+ m p Ans : since (n k) is a factor of x2 + px + q (n k)2 + p(n- k) + q = 0 And (n k)2 + m(n k) + n = 0 Solve this problem by yourself, k= n+ nq m p
SELF PRACTICE 16. If 2, 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) 4 3 2 18. What must be subtracted from 8x + 14x 2x + 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)