Find the values of k ε R subject to the following condition :

One root of $x^2 - 6x + k = 0$

** Option:**

**A.**2

**B.**0

**C.**1

**D.**8

**Answer: D . 8**

** Justification:**

Let the roots of the equation be α and β.

Also α = 2β

Now, $α + β = {-(-6)/1} = 6$

.`. 2β + β = 6

.`. 3β = 6

.`. β = 2

and

α = 2β

= (2)2

= 4

Also, αβ = $k/1 = k$

2(4) = k

k = 8.