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Let $a$ and $b$ be the solutions of the equation $2x^2-10x+5=0$. What is the value of $(2a-3)(4b-6)$?

 Jul 23, 2022
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By the quadratic formula, the solutions are (5 +/- sqrt(17))/2.

 

Plugging these in, we get

 

(2a - 3)(4b - 6) = (2*(5 + sqrt(17))/2 - 3)*(4*(5 - sqrt(17)/2 - 6) = -26.

 Jul 23, 2022

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