Question

if alpha and beta are zeros of f x is equals to 2 X square + 5 x + K such that Alpha square + b square + Alpha into beta is equals to 21/
4 find the value of k

Answer 1

α²+β²+αβ =21÷4       sum of zeros (α+β) = -b/a  product of zeros (αβ) = c/a

f(x)= 2x²+5x+k    a=2 b=5 c=k

α²+β²+αβ can be written as (α+β)²-αβ = 21/4

-5/2 - k/2 = 21/4 simplying we get k=-31/2