Question

Find a polynomial of the specified degree that has the given zeros. Degree 4; zeros −1, 1, 4, 5 P(x) =

Answer 1

The polynomial is;

x^4-9x^3+19x^2+9x-20

Explanation:

Since it has a degree of 4, the highest power is 4

We have four zeros

So this means that each of the linear factors are;

We get this by equating each of the terms to x

(x-1)(x+1)(x-4)(x-5)

(x-1)(x+1) = x^2-1

So we have

(x-4)(x^2-1)

= x^3-x-4x^2 + 4

And lastly, we have

x(x^3-x-4x^2 + 4)-5(x^3-x-4x^2+4)

So we have;

x^4-x^2-4x^3+4x-5x^3+5x+20x^2-20

x^4-9x^3+19x^2+9x-20