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 $7$

Let $\frac{a}{r},a,ar$are be the roots

$\Rightarrow \frac{a}{r}.a,ar=8$

$\Rightarrow a^3=8$

$\Rightarrow a=2$

$a=2$ is a root of given equation

$\Rightarrow 8-4k+28-8=0$

$\Rightarrow k=7$