Given that α, γ are roots of the equation Ax2−4x+1=0, and β, δ the roots of the equation of Bx2−6x+1=0, such that α,β,γ, and δ are in H.P., then

Since α,β,γ,δ are in H.P., 1/α,1/β,1/γ,1/δ are in A.P. and they maybe taken as a−3d,a−d,a+d,a+3d. Replacing x by 1/x, we get the equation whose roots are 1/α,1/β,1/γ,1/δ. Therefore, equation x2−4x+A=0 has roots a - 3d, a + d and equation x2−6x+B=0 has roots a - d, a + 3d. Sum of the roots is    2(a−d)=4,2(a+d)=6∴     a=5/2,d=1/2Product of the roots is(a−3d)(a+d)=A=3(a−d)(a+3d)=B=8