If the equation x2 + ax + b = 0 has distinct real roots and x2 + a|x| + b = 0 has only one real root, then which of the following is true?

Since the equation x2 + ax + b = 0 has distinct real roots and x2+a|x|+b=0 has only one real root, so one root of the equation x2+ax+b=0 will be zero and other root will be negative. Hence, b = 0 and a > 0.