Question

If the roots of the cubic equation $x^3-5x^2+kx-27=0$ are in G.P. then the value of $k$ is

• A. 15
• B. 12
• C. 9
• D. 6

Answer 1

Answer: (A)

Let roots be $\frac{a}{r}$, $a$, ar
$\frac{a}{r}+a+ar=5$ .....(1)
$\frac{a^2}{r}+a^2+a^{2}r=k$.....(2)
$a^3=27\Rightarrow a=3$ ....(3)
using $a=3$ in (1) and (2) we get
$k=15$