If a,b,c are three distinct positive real numbers then the  number of real roots of ax2+2b|x|−c=0 is

x=−2b±4b2+4ac2a a,b,c are positive. So, |x|=−b±b2+acx=±-b±b2+acx=-b+b2+ac, -b-b2+ac, b+b2+ac, b-b2+ac⇒x has two real values, neglecting x=−b−b2+ac, b-b2+ac  as |x|≥0