Question

Create a polynomial function that will have the roots: {-4,-2,3}, and also goes through the point (2,-6)

Answer 1

To get the polynomial function,

Given the roots (-4, -2, 3)

The general equation will be

`y=A(x+4)(x+2)(x-3)`

Since we are told that it passes through the point (2, -6)

Then, this means that x=2, y = -6

We will then substitute the values to get A

`-6=A(2+4)(2+2)(2-3)`

=>

`-6=A(6)(4)(-1)`

=>

`-6=-24A`

=>

`A=-(6)/(-24)=(1)/(4)`

=>

`A=(1)/(4)`

Therefore, the polynomial function is

`y=(1)/(4)(x+4)(x+2)(x-3)`

On simplifying further, we will obtain

`y=(1)/(4)(x^3+3x^2-10x-24)`