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Q.
If the equation $x^{2}+a x+b=0$ has distinct real roots and $x^{2}+a|x|+b=0$ has only one real root, then which of the following is true ?
Complex Numbers and Quadratic Equations
Solution:
Since the equation $x^{2}+a x+b=0$ has distinct real roots and $x^{2}+a|x|+b=0$ has only real root, so one root of the equation $x^{2}+a x+b=0$ will be zero and other will be negative. Hence, $b=0$ and $a>0$.
