"If a quadratic equation has roots 4 and -12, and the constant term is -144, what is the equation?" ~Anonymous

There are two ways you can go about solving this. I'll show you the method I like best. It's pretty straightforward, and makes use of two rules:

If the roots of a quadratic ax² + bx + c = 0 are x₁ and x₂, then x₁ + x₂ = -b/a, and x₁x₂ = c/a. These two rules will help you answer your question. We know the values of x₁ and x₂ (they are 4 and -12). We also know that c (the constant term) is -144. So we can rewrite these equations as follows:

4 + (-12) = -b/a; -8 = -b/a; b = 8a
4(-12) = -144/a; -48a = -144; a = 3

Plugging this into the first equation gives b = 8(3) = 24

Therefore, the equation is 3x² + 24x - 144 = 0