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Let e and d denote the solutions of 2x^2 + 3x - 5=0. What is the value of (d-1)(e-1)?

 Mar 13, 2023
 #1
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By the quadratic formula, the roots are x = -1 +/- sqrt(7/2)

 

Then (d - 1)(e - 1) = (-1 + sqrt(7/2) - 1)(-1 - sqrt(7/2) - 1) = 1/2.

 Mar 13, 2023
 #2
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Like so:

 

 Mar 13, 2023

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