Question

If 3 and -3 are two zeros of the polynomial (x4 + x3 - 11x? - 9x + 18), find
all the zeros of the given polynomial.
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Answer 1

Answer:

Let f(x)=x^4+x ^3 −11x ^2 −9x+18

Given : 3 and -3 are the zeroes of the polynomial (x+3) and (x−3) are factors of f(x), and consequently (x−3)(x+3)=(x^2−9) is factor of f(x)

Divide f(x) by (x^2−9) we get

Put f(x)=0

(x^2+x−2)(x^2−9)=0

(x−1)(x+2)(x−3)(x+3)=0

x=1 or x=−2 or x=3 or x=−3

hence all the zeros of the given polynomial are 1,−2,3 and −3.