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3 votes
Let $r$ and $s$ be the roots of $3x^2 + 4x - 12 = 0.$ Find $r^2 + s^2.$

User Gianni
by
6.6k points

1 Answer

3 votes

We can factorize the quadratic as


3x^2 + 4x - 12 = 3 (x - r) (x - s)

and expand the right side to get


3x^2 + 4x - 12 = 3x^2 - 3(r + s) x + 3rs


\implies r + s = -\frac43 \text{ and } rs = -4

Then we find


(r + s)^2 = r^2 + 2rs + s^2 \implies r^2 + s^2 = \left(-\frac43\right)^2 - 2(-4) = \boxed{\frac{88}9}

User Meisel
by
6.6k points
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