Question

Ans: 2
( alpha+beta=-frac{5}{2} ) and ( alpha beta=frac{k}{2} )
( alpha^{2}+beta^{2}+alpha beta=frac{21}{4} )
( Rightarrow(alpha+beta)^{2}-alpha beta=frac{21}{4} Rightarrow frac{25}{4}-frac{k}{2}=frac{21}{4} Rightarrow k=2 )

# If a, ß are the roots of the polynomial f(x) = 2x2 + 5x + k satisfying the relation o? +B+ QB = 27, then find the value of k for this to be possible.

Solution