0

Guest

Courses New

The sum of all the real roots of the equation |x – 2| 2 + |x – 2| - 2 = 0 is . . . . . . . . . . . . . . . . . . . . . . .

The sum of all the real roots of the equation |x – 2|2 + |x – 2| - 2 = 0 is . . . . . . . . . . . . . . . . . . . . . . .

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
|x – 2|2 + |x – 2| - 2 = 0
Case 1. x ≥ 2
⇒ (x – 2)2 + (x – 2) – 2 = 0
⇒ x2 – 3x = 0 ⇒ x(x – 3) = 0
⇒ x = 0, 3(0 is rejected as x ≥ 2)
⇒ x = 3 . . . . . . . . . . . . . . (1)
Case 2. X < 2
{ - (x – 2)}2 – (x – 2) – 2 = 0
⇒ x2 + 4 – 4x – x = 0 ⇒ (x – 1) (x – 4) = 0
⇒ x = 1, 4 (4 is rejected as x < 2)
⇒ x = 1 . . . . . . . . . . . . . (2)
Therefore, the sum of the roots is 3 + 1 = 4.

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More