Find the values of k ε R subject to the following condition :The ratio of the rots of $

Find the values of k ε R subject to the following condition :
The ratio of the rots of $x^2 + 3kx + 20 = 0$ is 4 : 5.

A. ± 3

B. - 3

C. + 3

D. - 1

E. None of the above

Answer: A. ± 3

Here If $x^2 + 3kx + 20 = 0$ has roots α and β,
then $α/β = 4/5$
.`. $α/4 = β/5 = {α + β}/9 = -3k/9 = -k/3$
.`. $α = {-4k}/3$ and .`. $β = {-5k}/3$
Now, αβ = $c/a = 20/1 = 20$
.`. $({-4k}/3) ({-5k}/3)$ = 20
.`. $k^2 = 9$
.`. $k = ± 3$

Posted in: Quadratic Equations - Algebra - Mathematics

Find the values of k ε R subject to the following condition :The ratio of the rots of $x^2 + 3kx + 20 = 0$ is 4 : 5.

Find the values of k ε R subject to the following condition :
The ratio of the rots of $x^2 + 3kx + 20 = 0$ is 4 : 5.