If $x^2 - 6x + α = 0 has two roots α, β and 3α + 2β = 20, then find a.
Answer: A. - 16
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