Question

The roots of the following quadratic equation is real and equal, find k.

 kx (x – 2) + 6 = 0

Answer 1

 kx (x – 2) + 6 = 0

\[\Rightarrow k x^2 - 2kx + 6 = 0\]

The roots of the given quadratic equation are real and equal. So, the discriminant will be 0.

\[b^2 - 4ac = 0\]
\[ \Rightarrow \left( - 2k \right)^2 - 4 \times k \times 6 = 0\]
\[ \Rightarrow 4 k^2 - 24k = 0\]
\[ \Rightarrow 4k\left( k - 6 \right) = 0\]
\[ \Rightarrow 4k = 0 \text{ or } k - 6 = 0\]
\[ \Rightarrow k = 0 \text{ or } k = 6\]

But k cannot be equal to 0 since then there will not be any quadratic equation.
So, k = 6