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Rational root theorem
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===Cubic equation=== The general [[cubic equation]] <math display="block">ax^3 + bx^2 + cx + d = 0</math> with integer coefficients has three solutions in the [[complex plane]]. If the rational root test finds no rational solutions, then the only way to express the solutions [[algebraic expression|algebraically]] uses [[Cubic function|cube roots]]. But if the test finds a rational solution {{math|''r''}}, then factoring out {{math|(''x'' β ''r'')}} leaves a [[quadratic polynomial]] whose two roots, found with the [[quadratic formula]], are the remaining two roots of the cubic, avoiding cube roots.
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