JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The sum of all the roots of the equation \( (x-1)^{2}-5|x-1|+6=0 \), is:
- A 4
- B 3
- C 1
- D 5
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
Let \( |x-1|=t \) \( t^{2}-5t+6=0\) \(\ t=2 \ \&\ t= 3 \) \( |x-1|=2\) \(\&\) \( |x-1|=3\) \(x-1 \pm 2\ \& \ x-1= \pm 3\) \(x=1 \pm 2\ \& \ x=1 \pm 3\) \(\therefore\) root \(=3,-1,4,-2\) ∴ Sum of root \(=3+(-1)+4+(-2)=4\).
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