Writing a quadratic equation given the roots and the leading coefficient

Question

roots are -2, -3 and coefficient is 4

use the letter x to represent the variable.

Answer 1

Hello Stephanie,

Lets start by writing the roots in factor form: (x+ 2) (x + 3).

Since we're told it is a quadratic equation we know the final form will be a x² + b x + c = 0

Lets FOIL the two factors:

( x + 2 ) ( x + 3 ) = x ² + 3 x + 2 x + 6 = x ² + 5x + 6 = 0 simplified.

Since the problem tells us that the (leading?) coefficient is 4 and ours is an implied 1, we must multiply every term by 4 to meet that condition.

4 ( 1 x ² + 5 x + 6 ) = 4 x ² + 20 x + 24 = 0 by using the Distributive Property.

Answer 2

If c is a root, then x - c is a factor.

So, f(x) = 4(x+2)(x+3) = 4(x² + 5x + 6) = 4x² + 20x + 24