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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