SOLUTION: If alpha,beta are the roots of the equation 2x^2+5x+k=0. Find the value of k if alpha^2+beta ^2+alpha*beta=21/4

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Question 837796: If alpha,beta are the roots of the equation 2x^2+5x+k=0. Find the value of k if alpha^2+beta ^2+alpha*beta=21/4
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have and , by Vieta's formulas.

Note that . So , or . This gives us k = 2.