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  • 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 .

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 .

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

      \ f(x) =2x^2+ 5x +k

herefore 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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Deependra Verma

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