Question

Find a polynomial f(x) of degree 5 that has the following zeros.

Answer 1

Answer:

$f(x)=(x-9)(x-4)(x+5)^2(x+7)$

Step-by-step explanation:

Answer 2

Answer:

$f (x) = (x-4)(x + 5)^2(x-9)(x+7)$

Step-by-step explanation:

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

In this case we know that the zeros are:

$x = 4,\ x-4 =0$

$x = 9,\ x-9=0$

$x = -5$, $x + 5 = 0$ (multiplicity 2)

$x = -7,\ x+7=0$

Now we can write the polynomial as a product of its factors

$f (x) = (x-4)(x + 5)^2(x-9)(x+7)$

Note that the polynomial is of degree 5 because the greatest exponent of the variable x that results from multiplying the factors of f (x) is 5