The roots α,β  of the equation x2−5x+a=0  are connected by the relation 3α+2β=12. Then the value of a  is

The given equation is x2−5x+a=0 α,β  are the roots of given equationSum of the roots : α+β=5  … ( 1 )Product of the roots : αβ=a  … ( 2 )and 3α+2β=12  … ( 3 )Solving the first and third equations, we get α=2  and  β=3  and hence, αβ=a⇒2(3)  =a ∴a=6