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

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1

4

3

2

answer is D.

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Detailed Solution

It is given that the quadratic equation

(m - 1) x^{2} - 2 (m - 1) x + 1 = 0

has real equal roots.
We know that for a quadratic equation the standard form,

a x^{2} + bx + c = 0

the formula for discriminant is

b^{2} - 4 ac

.
Comparing the given equation with the standard quadratic equation and substituting the values in the formula for discriminant ,
Discriminant =

{(- 2 (m - 1))}^{2} - 4 \times (m - 1)

Solving the above expression further we get the value of discriminant as,

4 m^{2} - 8 m + 4 - 4 m + 4

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

We neglect

m = 1

as the equation will not be quadratic anymore.
Hence,

m = 2 .

Hence, the correct option is 4.

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