## Ask Professor Puzzler

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"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 ax^{2} + bx + c = 0 are x_{1} and x_{2}, then x_{1} + x_{2} = -b/a, and x_{1}x_{2} = c/a. These two rules will help you answer your question. We know the values of x_{1} and x_{2 }(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 3x^{2} + 24x - 144 = 0