If α , β are roots of the equation ax2+bx+c=0 then the  equation whose roots are  2α+3β and 3α+2β is

We have,  α+β=−ba,αβ=caThe required equation is x2−5x(α+β)+(2a+3β)(3α+2β)=0⇒x2+5xba+6α2+β2+13αβ=0⇒x2+5bxa+6(α+β)2+αβ=0⇒x2+5bax+6b2a2+ca=0⇒a2x2+5abx+6b2+ac=0