SOLUTION: Find a degree 3 polynomial that has zeros -2, 3 and 6 and in which the coefficient of x^2 is -14? ok.. I know the zeros would be (x+2) (x-3) (x-6).. then I get lost with the -14

Question 975001: Find a degree 3 polynomial that has zeros -2, 3 and 6 and in which the coefficient of x^2 is -14?
ok.. I know the zeros would be (x+2) (x-3) (x-6).. then I get lost with the -14x^2..
can someone please help find what the polynomial is?
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39631) (Show Source): You can put this solution on YOUR website!
What? Just finish! The binomial product makes the zeros work. That product by itself has leading coefficient of 1. Just apply the factor, -14.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Any cubic polynomial with roots -2,3,6 will be of this form

where k is some constant

Let's expand out the polynomial

The x^2 term is

We want the x^2 coefficient to be -14, so, which means

Since k = 2, turns into after k is replaced with 2 and you simplify

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