examday

/TMUA

Let $a,b$ be real constants. Let $n$ be the number of real solutions to the equation $x^2-a|x|+b=0$. Which of the following statements are true?

• I. $n=4$ if and only if $a^2>4b>0$ and $a>0$
• II. $n=2$ only if $b\ge0$
• III. $n=0$ if $4b>a^2$