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If α and β are the zeroes of the polynomial f(x)=2x²+5x+k,satisfying the relation α²+β²+αβ=21÷4,then find the value of k,for this is to be possible.

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by KSJOSEPH

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by KSJOSEPH

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f(x)=2x²+5x+k

α²+β²+αβ=21÷4

α²+β²+αβ=(α+β)²-αβ

α+β= -b/a = -5/2

αβ=c/a = k/2

α²+β²+αβ=(-5/2)²-k/2

=25/4-k/2

α²+β²+αβ=21/4

21/4=25/4-k/2

21/4-25/4=k/2

-4/4=k/2

-1=k/2

k=-1×2

k=-2