Question

What polynomial has roots of −4, 1, and 6?

x^3 − 3x^2 − 22x + 24
x^3 − x^2 − 26x − 24
x^3 + x^2 − 26x + 24
x^3 + 3x^2 + 14x − 24

Answer 1

(X + 4)(x - 1)(x -6) = (x^2 - x + 4x -4)(x - 6)
(x^2 + 3x -4)(x - 6) = x^3 -6x^2 + 3x^2 - 18x - 4x + 24 = x^3 - 3x^2 - 22x + 24
It is the first one

Answer 2

(a)
`x^3-3x^2-22x+24`

Explanation:

roots are −4, 1, and 6

If a,b,c are the root then polynomial is (x-a)(x-b)(x-c)

Here -4, 1 and 6 are the roots, so polynomial becomes

(x-(-4)) (x-1) (x-6)

`(x+4) (x-1) (x-6)`

Multiply (x+4)(x-1)

`(x+4) (x-1) (x-6)`

`(x^2+3x-4) (x-6)`

`x^3-6x^2+3x^2-18x-4x+24`

`x^3-3x^2-22x+24`