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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
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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

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