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

Guest Aug 6, 2022

#1**0 **

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 \(b = -{12 \over 7}\).

BuilderBoi Aug 6, 2022