Question

Write a quadratic function h whose only zero is - 1.
h(x) -

Answer 1

Answer: Either h(x) = (x+1)^2 or h(x) = x^2+2x+1

Reason:

If x = -1 is a root, then x+1 = 0 and it shows (x+1) is a factor.

We'll have two copies of the factor (x+1) because it's the only root. We call it a double root or a root of multiplicity 2.

That leads to h(x) = (x+1)^2 as one possible answer.

Expanding things out leads to this:

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

h(x) = (x+1)(x+1)

h(x) = x(x+1)+1(x+1)

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

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

It shows that h(x) = (x+1)^2 is the same as h(x) = x^2+2x+1