Question

The polynomial p(x) = x³– 5x² – x + 5 is such that p (1) = 0 and p (-1) = 0. Which of these is equivalent to p(x)?

Answer 1

Step-by-step explanation:

p(x)=x 3 −5x 2 −16x+80

Let α,β,γ are the zeroes of polynomial p(x) such that α+β=0.

Then,

Sum of zeros = − Coefficient of x 3Coefficient of x 2α+β+γ=50+γ=5γ=5

Also,

Product of zeros = − Coefficient of x 3Constant termαβγ=−80−5α 2 =−80α 2 =16α=±4Now,α+β=0⟹±4+β=0β=∓4

Thus,

zeros of the given polynomial are 4,−4,5.

Hope this will help you buddy...

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