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MathNet 2015-part-01 — 191 problems (EN–VI) Question 95

Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)

Question 95

Numbers $x_1$, $x_2$, $x_3$ ($x_1 \lt x_2 \lt x_3$) are the roots of the equation
$$
x^3 - 3x^2 + (a+2)x - a = 0,
$$
where $a$ is a real number.
Find all possible values of the expression $4x_1 - x_1^2 + x_3^2$.