Question

If function $f\left(x\right)=|x^2+a|x|+b|$ has exactly three points of non differentiability then which of the following can be true

• A. $b=0,a<0$
• B. $b<0,a\in R$
• C. $b>0,a\in R$
• D. all of these

Answer 1

The correct option is A $b=0,a<0$

$f\left(x\right)=|x^2+a|x|+b|$ has the three point of non differentiability then Quadratic $x^2+ax+b=0$ must have one root at origin and other root (+)ve
$\Rightarrow b=0anda<0$