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MathNet 2019-part-04 — 184 problems (EN–VI) Question 28

Math Olympiad Vault · MathNet 2019-part-04 — 184 problems (EN–VI)

Question 28

Find all values of the real parameter $a$ for which all solutions of the equation
$$
x^{4}-2 x^{3}-3 x^{2}-4 a x-a^{2}=0
$$
are real. For the values found, solve the equation.