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

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

=>

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

=>

$-6=-24A$

=>

$A=-\frac{6}{-24}=\frac{1}{4}$

=>

$A=\frac{1}{4}$

Therefore, the polynomial function is

$y=\frac{1}{4}(x+4)(x+2)(x-3)$

On simplifying further, we will obtain

$y=\frac{1}{4}(x^3+3x^2-10x-24)$