First slide

Theory of equations

Question

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?

Moderate

A

b = 0, a > 0
B

b = 0, a < 0
C

b > 0, a < 0
D

b < 0, a > 0

Solution

Since the equation x² + ax + b = 0 has distinct real roots and $x^{2} + a | x | + b = 0$ has only one real root, so one root of the equation $x^{2} + ax + b = 0$ will be zero and other root will be negative. Hence, b = 0 and a > 0.

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