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An Equation

Source: 1981 National High School Mathematics League, Problem 7

February 20, 2020

Problem Statement

The equation x∣x∣+px+q=0x|x|+px+q=0 is given. Which of the following is not true? (A)\text{(A)}It has at most three real roots. (B)\text{(B)}It has at least one real root. (C)\text{(C)}Only if p2−4q≥0p^2-4q\geq0 ,it has real roots. (D)\text{(D)}If p<0p<0 and q>0q>0, it has three real roots.
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