Question

Find a polynomial equation that has double zeros at x = -3, and x = 4

Answer 1

A double zero occurs in a polynomial when a factor is repeated, or in other words, squared. Since the polynomial has double zeros, then, we get

`f(x)=(x+3)^2(x-4)^2`

By expanding this result, we have

`f(x)=(x^2+6x+9)(x^2-8x+16)`

which gives

`f(x)=x^4-8x^3+16x^2+6x^3-48x^2+96+9x^2-72x+144`

By combining similar terms, we have