Answer:
3x² + 24x + 36 = 0
Explanation:
A quadratic equation has the standard form ax² + bx + c = 0.
a, b and c are constants.
The roots of a quadratic equation represent the two solutions to the quadratic equation
Given that the roots are -2 and -6 we have
x = -2 and x = -6 as the solutions
Add 2 to both sides of x = -2 ==> x + 2 = 0
Add 6 to both sides of x = -6 ==> x + 6= 0
So (x+2)(x+6) = 0 is the factored representation of this equation. We have to multiply by a leading coefficient of 3
So the quadratic equation is
3(x+2)(x+6) = 0
Using the FOIL method
(x + 2)(x + 6) = x² + 6x + 2x + 12 = x² + 8x + 12
The leading coefficient is the coefficient of x² and is given as 3
So the quadratic equation in standard form is
3(x² + 8x + 12) = 0
==> 3x² + 24x + 36 = 0
If you solve this equation on a quadratic equation calculator you will get the solutions x = -2 and x=-6