If α and β are the roots of equation 2x2 - 5x + 7 = 0, then the equation whose roots are 2α + 3β and 3β + 2β, is

Since, α and β be the roots of the equation2x2 -5x+ 7 =0,thenα+β=52 and αβ=72Now sum of roots = (2α+3β)+(3α+2β)=5(α+β)=252and product of roots  =(2α+3β)(3α+2β)=6α2+β2+13αβ=6(α+β)2−2αβ+13αβ=6×254−7+912=41The required equation isx2−252x+41=0⇒ 2x2−25x+82=0