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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 :
The ratio of the rots of $x^2 + 3kx + 20 = 0$ is 4 : 5.

Option:
A. ± 3
B. - 3
C. + 3
D. - 1
Answer: A . ± 3

Justification:

Here If $x^2 + 3kx + 20 = 0$ has roots α and β,
then $α/β = 4/5$
.`. $α/4 = β/5 = {α + β}/9 = -3k/9 = -k/3$
.`. $α = {-4k}/3$ and .`. $β = {-5k}/3$
Now, αβ = $c/a = 20/1 = 20$
.`. $({-4k}/3) ({-5k}/3)$ = 20
.`. $k^2 = 9$
.`. $k = ± 3$

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