# If a and b the zeros of the polynomial f(x) = 2x^2 + 5x + k , satisfying the relation a^2 + b^2 +ab = 21/4 ,then find the value of k for this to be possible .

Solution: Since a and b are the zeros of the polynomial

$\\ f(x) =2x^2+ 5x +k$

$\therefore a+b = -5/2 , ab=k/2$

Now ,

$\\ a^2 +b^2 +ab = 21/4$

$\\\Rightarrow ( a^2 +b^2 +2ab) -ab=21/4 \\ \\ \Rightarrow (a-b)^2-ab=21/4\\ \\ \Rightarrow (25/4-k/2)=21/4 \\ \\ \Rightarrow k=2$

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