Find $m$ , if the quadratic equation $(m - 1) x^{2} - 2 (m - 1) x + 1 = 0$ has real equal roots.

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Solution

The correct option is B $2$
For the quadratic equation, $(m - 1) x^{2} - 2 (m - 1) x + 1 = 0$
Discriminant = ${(- 2 (m - 1))}^{2} - 4 \times (m - 1) = 0$ ...... Since roots are real equal roots
$4 m^{2} - 8 m + 4 - 4 m + 4 = 0$
$4 m^{2} - 12 m + 8 = 0$
$m^{2} - 3 m + 2 = 0$
$∴ m = 1, 2$
Neglect $m = 1$ as the equation will not be quadratic anymore.
Hence, $m = 2$

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