Question

Without solving, determine the character of the solutions of the quadratic equation in the complex number system.

Answer 1

Given equation:

$9x^2-6x+1=0$

By using middle term factirization we get,

$\begin{gathered} 9x^2-6x+1=0 \\ 9x^2-3x-3x+1=0 \\ 3x(3x-1)-1(3x-1)=0 \\ (3x-1)(3x-1)=0 \end{gathered}$$\begin{gathered} (3x-1)^2=0 \\ x=\frac{1}{3},\frac{1}{3} \end{gathered}$

So, the roots are real and same.

Thus, the equation have a repeated real rools.

Answer: Option (A)