Question

Write a polynomial equation with integer coefficients that has the given roots.

x=0
, x=−1
, x=−3

Answer 1

Answer: y = x³ + 4x² + 3x

Explanation:

We are given that this equation has the roots 0, -1, and -3. To write these as factors, we will write them like this:

y = (x)(x + 1)(x + 3)

Now, we will turn this into a polynomial equation by distributing the factors above out. This gives us a cubic polynomial equation.

y = (x)(x + 1)(x + 3)

y = (x² + x)(x + 3)

y = x³ + 4x² + 3x