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Find the constants a and b such that x = -1 and x = 7 are both solutions to the equation ax^2 + bx + 2 = 0.

 Aug 6, 2022
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By Vieta's, the product of the roots is \({c \over a} = {2 \over a}\). We know that the product of the roots is \(-7\), so we have the equation \({2 \over a} = -7\).

 

Solving the equation yields \(a = -{2 \over 7}\).

 

Also, we know that the sum of the roots is \({b \over {-{2 \over 7}}} = 6\), meaning \(b = -{12 \over 7}\).

 Aug 6, 2022

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