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

Without solving, determine the character of the solutions of the quadratic equation-example-1

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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=(1)/(3),(1)/(3) \end{gathered}

So, the roots are real and same.

Thus, the equation have a repeated real rools.

Answer: Option (A)

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