If the roots of the equation 8x3−14x2+7x−1=0 are in G.P., then the roots are
1, 12, 14
Let the roots be αβ,α,αβ,β≠0
Then the product of roots is α3=−−18=18
⇒ α=12 and hence β = 12
(Since, sum of roots =αβ+α+αβ=14/8),
so roots are 1,12, 14
Alternate method: By inspecting through options, we get the numbers 1,12, 14 satisfying the given equation.