Find m if the quadratic equation m-1×2-2(m-1)x+1=0 has equal roots.

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

A
1
B
2
C
3
D
4

Solution:

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

has equal roots.

\Rightarrow D = 0

\Rightarrow B^{2} - 4 AC = 0

\Rightarrow {[- 2 (m - 1)]}^{2} - 4 \times (m - 1) \times 1 = 0

\Rightarrow 4 {(m - 1)}^{2} - 4 (m - 1) = 0

\Rightarrow 4 (m - 1) (m - 1 - 1) = 0

\Rightarrow m - 1 = 0

and

m - 2 = 0

\Rightarrow m = 1

and

m = 2

But for m = 1, the given quadratic equation does not exist.
Thus, m = 2.

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