Question

Please help me out!!!!!

Answer 1

Given:

The zeros of the polynomial are $-2,\pm 5,4$.

Degree = 4

Leading coefficient  = 1

To find:

The polynomial.

Solution:

If c is a zero of a polynomial, then (x-c) must be a factor of the polynomial.

Here, -2,4,-5, 5, are zeros of the required polynomial, so (x+2), (x-4), (x+5), (x-5) are factors of required polynomial.

$p(x)=(x+2)(x-4)(x+5)(x-5)$

$p(x)=(x^2-4x+2x-8)(x^2-5^2)$     $[\because a^2-b^2=(a-b)(a+b)]$

$p(x)=(x^2-2x-8)(x^2-25)$

Using distributive property, we get

$p(x)=x^2(x^2-25)-2x(x^2-25)-8(x^2-25)$

$p(x)=x^4-25x^2-2x^3+50x-8x^2+200$

On combining like terms, we get

$p(x)=x^4-2x^3+(-25x^2-8x^2)+50x+200$

$p(x)=x^4-2x^3-33x^2+50x+200$

Here, the leading coefficient is 1. So, it is the required polynomial.

Therefore, the correct option is E.