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Solution of quadratic equations, Relation between roots and coefficients (only real roots to be considered). Practical problem on quadratic equations.

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.

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