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Let r and s be the roots of 3x^2 + 4x + 12 = 2x^2 - 7x + 5.  Find r^2 + s^2.

 May 24, 2021
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Let r and s be the roots of 3x2+4x+12=2x27x+5.
Find r2+s2.

 

3x2+4x+12=2x27x+53x22x2+4x+7x+125=0x2+11x+7=0

 

Vieta: rs=7, (r+s)=11

(r+s)=11r+s=11(r+s)2=(11)2r2+2rs+s2=121|rs=7r2+27+s2=121r2+s2=12114r2+s2=107

 

laugh

 May 24, 2021

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