Question

Which polynomial equation of least degree has -2, -2, 3, and 3 as four of its roots?

Answer 1

x^4 -2x^3 -11x^2 + 12x + 36

The factors would be (x + 2)(x + 2)(x -3)(x-3) OR (x + 2)^2(x-3)^2
multiply all of the factors to get the 4th power polynomial

Answer 2

`x^(4)-2x^(3)-11x^(2)+12x+36`

Explanation:

The polynomial which have four roots that means zero roots of this polynomial will be (x -2), (x -2), (x -3) and (x -3)

So the polynomial will be (x + 2)(x + 2)(x - 3)(x - 3)

= (x + 2)²(x - 3)²

= (x² + 4x + 4)(x² + 9 - 6x)

=
`x^(4)+4x^(3)+4x^(2)+9x^(2)+36x +36-6x^(3)-24x^(2)-24x`

=
`x^(4)-2x^(3)-11x^(2)+12x+36`

Therefore, the polynomial will be (
`x^(4)-2x^(3)-11x^(2)+12x+36`)