Question

The number of distinct real roots of |x||x + 2| - 5|x + 1| - 1 = 0 equals to _____.

Answer 1

Correct answer: 3

(I) x ≥ 0

x² + 2x – 5x – 5 – 1 = 0

x² – 3x – 6 = 0 → 1 root +ve

(II) –1 ≤ x < 0

–x² – 2x – 5x – 5 – 1 = 0

x² + 7x + 6 = 0 → x = –1 is a root

(III) –1 < x ≤ –2

x² – 2x + 5x + 5 – 1 = 0

x² – 3x – 4 = 0 → No root in given range

(IV) x < –2

x² + 2x + 5x + 5 – 1 = 0

x² + 7x + 4 = 0 → One root less than – 2

\(\therefore\) The number of distinct roots are 3.