If the ratio of the roots of the equation $x^2 + 6x + k - 5 = 0$ is 3:5, then find the value of k.

** Option:**

**A.**$52/15$

**B.**$52/18$

**C.**$55/16$

**D.**$50/16$

**Answer: C . $55/16$**

** Justification:**

Suppose the roots of the equation $x^2 - 6x + k + 5 = 0$ be α and β such that α < β.

Here, a = 1, b = - 6, c = k + 5

$α + β = {-b}/a = 6 $ and $ αβ= c/a = {k + 5}/1 = k + 5 $

Since the ration of the roots is 3:5 $α/β = 3/5$

.`. $α/3 = β/5$

Each ration = $ {α + β}/8$

= $6/8 = 3/4$

.`.$α/3 = 3/4 → α = 9/4 $ and $ β/5 = 3/4 → β = 15/4 $

Now, α.β = k + 5

.`. $9/4$.$15/4 = k + 5$

.`. 135 = 16k + 80

.`. 16k = 135 - 80

.`. 16k = 55

.`. $k = 55/16$