Question

A polynomial function with leading coefficient `a` has zeroes of multiplicity one at `x = -2` and `x = 1` and a zero of multiplicity two at `x = 2`. What is the equation of this polynomial function?

Answer 1

`y = a(x +2)(x - 1)(x - 2)^2` will be the equation, where `a` is a real number.

Explanation:

The zeroes of multiplicity `n` will have exponent `n`.

`y = a(x +2)(x - 1)(x - 2)^2`

Where `a` is the vertical stretch/compression. This will influence the placement of the y-intercept. I haven't specified the value of `a` because the y-intercept isn't given .

I'll leave you the task to multiply it out into standard form. If you don't know what standard form is take a look here:

Standard form of `(x - 3)(x - 2)` would be `x^2 - 5x + 6`, or the expanded version of the expression.

Hopefully this helps!