Question

degree 4, x=-1, x=1/5 are both zeros with multiplicity 2. What is the expression for the plynomial p(x) with these numbers?

Answer 1

p(x) = (x + 1)²(5x - 1)²

Explanation:

Since we are given the 2 zeroes, we put them into binomial form:

(x + 1)(5x - 1)

We are also given that we have the polynomial degree of 4, and both zeroes have a multiplicity of 2. Therefore, both roots are powered by 2:

(x + 1)²(5x - 1)²

When we multiply it out, we should get a polynomial with a degree of 4.