If the sum of the roots of the equation $x^2 + 8x + 2 - k = 0$ is twice the product of the roots.

Then find k.

** Option:**

**A.**2

**B.**4

**C.**8

**D.**6

**Answer: D . 6**

** Justification:**

Suppose the roots of the equation $x^2 + 8x + 2 - k = 0$ be α and β such that α < β.

Here, a = 1, b = 8 and c = 2 - k

.`.$α + β = {-b}/a = -8$

and

.`.$αβ = c/a = {2 - k}/1 = 2 - k$

Here, the sum of the roots is double the product of the roots.

.`. α + β = 2αβ

.`. - 8 = 2(2 - k)

.`. - 4 = (2 - k)

.`. k = 6