Question

Polynomial equation when zeros are -4, -2, 1, 4

Answer 1

The required poynomial equation is $x^{4}+x^{3}-18x^{2}-16x+32$.

Step-by-step explanation:

Given,

The zeros of the polynomial are - 4, - 2, 1 and 4

To find, the polynomial equation = ?

We know that,

The polynomial equation = (x - A)(x - B)(x - C)(x - D)

= (x + 4)(x + 2)(x - 1)(x - 4)

= [(x + 4)(x - 4)] [(x + 2)(x - 1)]

= ($x^{2}-16$)($x^2-x+2x-2$)

=  ($x^{2}-16$)($x^2+x-2$)

= $x^{4}+x^{3}-2x^{2}-16x^{2}-16x+32$

= $x^{4}+x^{3}-18x^{2}-16x+32$

Thus, the required poynomial equation is $x^{4}+x^{3}-18x^{2}-16x+32$.