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.

** Option:**

**A.**± 3

**B.**- 3

**C.**+ 3

**D.**- 1

**Answer: A . ± 3**

** Justification:**

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

.`. $k^2 = 9$

.`. $k = ± 3$