First slide

Theory of equations

Question

If the roots of the equation $8 x^{3} - 14 x^{2} + 7 x - 1 = 0$ are in G.P., then the roots are

Moderate

A

$1, \frac{1}{2}, \frac{1}{4}$
B

$2, 4, 8$
C

$3, 6, 12$
D

None of these

Solution

Let the roots be $\frac{α}{β}, α, αβ, β \neq 0 .$ Then the product of roots is $α^{3} = - \frac{- 1}{8} = \frac{1}{8} \Rightarrow α = \frac{1}{2}$ and hence $β = \frac{1}{2},$ so roots are $1, \frac{1}{2} . \frac{1}{4}$

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