Question

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

• A. -3
• B. 7
• C. 4
• D. 0

Answer 1

Answer: (B)

Given equation is
$x^3-k{x}^2+14x-8=0$
According to the question,
$\frac{a}{r},a$ and $ar$ is the roots of equation.
Then, $\frac{a}{r}\cdot a\cdot ar=\frac{D}{A}$
$\Rightarrow \frac{a}{r}\cdot a\cdot ar=8\Rightarrow a^3=8$
$\Rightarrow a=2$
Since, $a=2$ is a root of given equation.
$\therefore (2{)}^3-k(2{)}^2+14(2)-8=0$
$\Rightarrow 8-4k+28-8=0$
$\Rightarrow k=7$