Question

2
select the correct answer from the drop-down menu.
find the polynomial.
{ -1/3, 4 } is the solution set of
3x^2 - 11x + 4 = 0
3x^2 - 11x - 4 = 0
(1/3)x^2 - 11x - 4 = 0
(-1/3)x^2 - 11x - 4 = 0

Explanation:

Step1: Write factors from roots

If roots are $x = -\frac{1}{3}$ and $x = 4$, then factors are $(3x + 1)$ and $(x - 4)$ (multiply first factor by 3 to eliminate fraction).

Step2: Multiply factors

$$(3x + 1)(x - 4) = 3x^2 - 12x + x - 4 = 3x^2 - 11x - 4$$

Step3: Form equation

Set polynomial equal to 0: $3x^2 - 11x - 4 = 0$

Answer:

3x² - 11x - 4 = 0