Question

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

Answer 1

Answer:

$f(x)=x(x-7)(x+8)^2$

Step-by-step explanation:

The zeros of the polynomial are all the values of $x$ for which the function $f(x)=0$

Therefore,

$x = 0$

$x = -8 \implies x + 8 = 0$ (twice)

$x = 7 \implies x -7 = 0$

Write the polynomial as a product of its factors:

$f(x)=x(x-7)(x+8)^2$