Question

The value of k, of the roots of the equation ${\text{2k}}{{\text{x}}^2} + {\text{2kx + 2 = 0}}$ are equal is
$
  {\text{A}}{\text{. }}\dfrac{4}{5} \\
  {\text{B}}{\text{. 4}} \\
  {\text{C}}{\text{. 1}} \\
  {\text{D}}{\text{. 0}} \\
$

Answer 1

Hint: To determine the value of k using the given equation, we apply the formula for roots of the quadratic equation and solve for the answer.

Complete step-by-step answer:

Given data, the equation ${\text{2k}}{{\text{x}}^2} + {\text{2kx + 2 = 0}}$ has equal roots.
If quadratic equation ${\text{a}}{{\text{x}}^2} + {\text{bx + c = 0}}$ has equal roots then the roots of the equation are $\sqrt {{{\text{b}}^2} - {\text{4ac}}} = 0$
Comparing it with the given equation, we get a = 2k, b = 2k, c = 2.
⟹$\sqrt {{{\text{b}}^2} - {\text{4ac}}} = \sqrt {{{\left( {{\text{2k}}} \right)}^2} - 4\left( {{\text{2k}}} \right)2} $= 0.
⟹${\text{4}}{{\text{k}}^2} - 16{\text{k = 0}}$
⟹k = 0, 4.
We ignore k = 0, because if k = 0 then it would not be quadratic.
Hence, k = 4.
Option B is the right answer.

Note: In order to solve this type of question the key is to figure out a way to find out the roots of the given quadratic equation. We pick an apt formula to compute the roots according to the given equation and then solve it to get the answer.