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) (Show Source): You can put this solution on YOUR website!
We have 
and 
, by Vieta's formulas.
Note that ^2 - \alpha \beta)
. So ^2 - \frac{k}{2} = \frac{21}{4})
, or 
. This gives us k = 2.
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