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

Guest Apr 24, 2020

geno3141 · Answer 1 · 2020-04-24T09:19:07

3x² + 4x + 12 = 0

Using the quadratic formula with a = 3 b = 4 c = 12:

x = [ -4 +/- sqrt( 4² - 4·3·12 ) ] ( 2·3 ) = ( -2 + 4sqrt(2) ) / 3 ( -2 - 4sqrt(2) ) / 3

[ ( -2 + 4sqrt(2) ) / 3 ]² + [ ( -2 - 4sqrt(2) ) / 3 ]²

= ( 36 - 16sqrt(2) ) / 9 + ( 36 + 16sqrt(2) ) / 9 = 8