Question

If the roots of $x^3-k{x}^2+14x-8=0$ are in geometric progression, then $k=$

• A. $-3$
• B. $7$
• C. $4$
• D. $0$

Answer 1

The correct option is B $7$

Since, roots of given equation are GP, $\frac{a}{r},a,ar$ (say)

Therefore, we have

Product of roots $=8$

$\Rightarrow \frac{a}{r}\times a\times ar=8\Rightarrow a^3=8\Rightarrow a=2$
$a=2$ is a root of the given equation
$\Rightarrow 8-4k+28-8=0\Rightarrow k=7$