Find the values of k ε R subject to the following condition :
One root of $x^2 - 6x + k = 0$

Answer: D. 8

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.

Posted in:  Quadratic Equations -  Algebra -  Mathematics