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

If the roots of the equations $x^2 + 3kx + 2 = 0$ are in the ratio of 1 : 2, then find the value of k.

Option:
A. 1
B. ± 1
C. 0
D. - 2
Answer: B . ± 1

Justification:

If α and β are the roots of the equation
$x^2 + 3kx + 2 = 0$, then $α + β = {-b}/a = {-3k}/1 = -3k$
and $αβ = c/a = 2/1 = 2$
also $α/β = 1/2$ is given.
.`. 2α = β
Now, α + β = -3k  and  αβ = 2
.`. α + 2α = -3k and α(2α) = 2
.`. 3α = -3k  and .`. $α^2 = 1$
.`. k = -α and α = -1
and k = -1 and α = 1
Thus, k = ±1

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