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