If the roots of the equations $x^2 + 3kx + 2 = 0$ are in the ratio of 1 : 2, then find the value of k.

** Option:**

**A.**1

**B.**± 1

**C.**0

**D.**- 2

**Answer: B . ± 1**

** Justification:**

If α and β are the roots of the equation

$x^2 + 3kx + 2 = 0$, then $α + β = {-b}/a = {-3k}/1 = -3k$

and $αβ = c/a = 2/1 = 2$

also $α/β = 1/2$ is given.

.`. 2α = β

Now, α + β = -3k and αβ = 2

.`. α + 2α = -3k and α(2α) = 2

.`. 3α = -3k and .`. $α^2 = 1$

.`. k = -α and α = -1

and k = -1 and α = 1

Thus, k = ±1