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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 $x^2 - 6x + α = 0 has two roots α, β and 3α + 2β = 20, then find a.

Option:
A. - 16
B. 8
C. 4
D. - 2
Answer: A . - 16

Justification:

Here, one root of the equation $x^2 - 6x + k - 3 = 0$ is the complex number 3 + 2i.
Hence the root is 3 - 2i.
Now, product of the roots : $c/a = {k - 3}/1 = k  - 3$
.`. k - 3 = (3 + 2i)(3 - 2i)
.`. k - 3 = $9 - 4i^2$
.`. k - 3 = 9 - 4
.`. k = 16

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