Question

Find a polynomial f(x) of degree 4 that has the following zeros.

-6, -9, 0, 7

Answer 1

f(x) =
`x^(4)` + 8x³ - 51x² - 378x

Explanation:

Given the polynomial has zeros x = - 6, x = - 9, x = 0, x = 7, then

The factors are (x + 6), (x + 9), x , (x - 7)

and f(x) is the product of it's factors, that is

f(x) = x(x + 6)(x + 9)(x - 7) ← expand the last pair using FOIL

= x(x + 6)(x² + 2x - 63)

= (x² + 6x)(x² + 2x - 63) ← distribute

=
`x^(4)` + 2x³ - 63x² + 6x³ + 12x² - 378x

=
`x^(4)` + 8x³ - 51x² - 378x