Math CentralQuandaries & Queries


Question from Sarah, a student:

How do you find the quadratic formula when you're given just the roots ... X=-3 X= 1/3

Thanks !


You aren't looking for "the quadratic formula" here (that's the thing that starts "minus b plus or minus root b squared..."), you're looking for the equation of a quadratic with these roots.

A product is equal to 0 if and only if one (or more) factor(s) is equal to zero. So the quadratic must have a linear factor that is equal to 0 when X=-3 and one that's equal to 0 when X= 1/3.

For what a is a + (-3) = 0?

For what b is b + 1/3 = 0?

Verify that (a+x)(b+x) has the properties you want.

What about k(a+x)(b+x) for some nonzero k?

Good Hunting!

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