Question

URGENT! Quarter ends tonight!

Write the polynomial function, in standard form, that has zeros -3, 4, and 1.

Answer 1

Answer:
`x^(3)` - 2
`x^(2)` - 11x + 12 = 0

Explanation:

Since the zeros of the polynomials are -3 , 4 and 1 , then the equation will be in the form:

(x+3)(x-4)(x-1) = 0

Expanding (x+3)(x-4) , we have

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

⇒
`x^(2)` -x - 12

combining with (x-1) , we have

(
`x^(2)` -x - 12) ( x -1 ) = 0

expanding , we have :

`x^(3)` -
`x^(2)`-
`x^(2)` + x - 12x + 12 = 0

⇒
`x^(3)` - 2
`x^(2)` - 11x + 12 = 0