Question

Write a polynomial function in standard form for the given set of roots.

-3,0,0.1
O A. f(x) = -3x + x²
O B. f(x) = -3x² + 1
O c. f(x) = x + 2x² – 3x²
O D. f(x) = x² – 3x² + x²
What is the answer?

Answer 1

`f(x) = {x}^(4) +4 {x}^(3) + 3 {x}^(2)`

Explanation:

Let f(x) be the polynomial.

If x=-3, x=0,x=0, x=1 are roots ,then by the factor theorem, x+3=0,x=0,x=0, x+1=0 are factors of f(x).

This implies that:

`f(x) = (x + 3)(x)(x)(x + 1)`

`f(x) = {x}^(2) ( {x}^(2) + x + + 3x + 3)`

`f(x) = {x}^(2) ( {x}^(2) +4x + 3)`

Expand further to get:

`f(x) = {x}^(4) +4 {x}^(3) + 3 {x}^(2)`