Question

If alpha and bita are zeroes of polynomial p(x)2x^2 + 5x + k statisfying the relation alpha square +bita square + alpha×bita = 21/4 . Then find the value of k

Answer 1

Heya

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Alfa + Beta = -5/2

And

Alfa × Beta = k/2

=>

Alfa² + Beta² + Alfa × Beta = 21/4

=>

( Alfa + Beta )² - Alfa × Beta = 21/4

=>

(25/ 4 ) -( k/2 ) = 21/4

=>

25 - 2k = 21

=>

-2k = 21 - 25



=>


-2k = -4



=>



k = 2