The sum of all the roots of the equation ( x - 1 ) 2 - 5 | x - 1 | + 6 = 0 is [2026]

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Solution

Q.
The sum of all the roots of the equation ${(x - 1)}^{2} - 5$ $| x - 1 |$ $+ 6 = 0$ is [2026]

1 1

2 3

3 5

4 4

Ans.
(4)

$Let | x - 1 | = t$

$t^{2} - 5 t + 6 = 0$

$t = 2 and t = 3$

$| x - 1 |$ $= 2 and$ $| x - 1 |$ $= 3$

$x - 1 \pm 2 and x - 1 = \pm 3$

$x = 1 \pm 2 and x = 1 \pm 3$

$∴$ $Roots are 3, - 1, 4, - 2$

$∴$ $Sum of roots = 3 + (- 1) + 4 + (- 2) = 4$

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