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# Algebra

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r and s are the roots of 3x^2 + 4x + 12 = 2x^2 - 8x + 7. Find r^2+s^2

May 31, 2022

#1
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We can simplify the expression to: $$x^{2}+12x+5=0$$.

By Vieta's formula, the sum of the roots ($$r + s$$), equals $${-12 \over 1} = -12$$, and the product of the roots ($$r \times s$$) equals $${5 \over 1 } = 5$$.

Note that $$r^2 + s^2 = (r+s)^2 - 2rs$$

Can you take it from here?

May 31, 2022