Question

Write a polynomial function of least degree that has the given zeros.1, -3, 4

Answer 1

GIVEN

The zeros of the polynomial are given to be 1, -3, and 4.

SOLUTION

Let the equation be in terms of x.

The roots of the equation are given to be:

`x=1,x=-3,x=4`

Recall that if a polynomial has a root x = a, a factor of the polynomial will be (x - a).

Therefore, the factors of the given polynomial will be:

`(x-1),(x+3),\text{ }and\text{ }(x-4)`

The function can be gotten by multiplying the factors:

`f(x)=(x-1)(x+3)(x-4)`

Expand the polynomial. Hence, the function is given to be:

`f(x)=x^3-2x^2-11x+12`