Set of all a ∈ R for which equation x | x -1|+| x +2|+a=0 has exactly one real root is:

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4-2.Quadratic Equations and Inequations

hard

The set of all $a \in R$ for which the equation $x | x -1|+| x +2|+a=0$ has exactly one real root is:

A

$(-6,-3)$

B

$(-\infty, \infty)$

C

$(-6, \infty)$

D

$(-\infty,-3)$

(JEE MAIN-2023)

Solution

$f(x)=x|x-1|+|x+2|$

$x|x-1|+|x+2|+a=0$

$x|x-1|+|x+2|=-a$

All values are increasing.

Standard 11

Mathematics

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