Quadratic EquationMedium
Question
The sum of all the roots of the equation $(x - 1)^{2} - 5|x - 1| + 6 = 0$, is:
Options
A.4
B.3
C.1
D.5
Solution
Let $|x - 1| = t$
$${t^{2} - 5t + 6 = 0 }{t = 2\& t = 3 }{|x - 1| = 2\&|x - 1| = 3 }{x - 1 \pm 2\& x - 1 = \pm 3 }{x = 1 \pm 2\& x = 1 \pm 3 }$$∴ $root = 3, - 1,4, - 2$
∴ Sum of root $= 3 + ( - 1) + 4 + ( - 2) = 4$.
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