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melomori [17]
3 years ago
6

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

Mathematics
1 answer:
jek_recluse [69]3 years ago
4 0
<h2>The required poynomial equation is x^{4}+x^{3}-18x^{2}-16x+32.</h2>

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.

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