How to check by a fixed algorithm/formula for the possibility of these: x^2 + x + 1 = 0 AND 2x^2 + 4x - 2 = 0 AND x^3 + 3 = 0
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1Do you mean those particular equations, or generic ones with arbitrary coefficients? Also, the 3rd one is not a quadratic. – dxiv Nov 17 '16 at 07:13
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Why not just use the Quadratic formula? https://en.wikipedia.org/wiki/Quadratic_formula – JB King Nov 17 '16 at 07:18
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all three of the siultaneously? Use quadratic equation to solve one and see if it satisfies the others. 1st: $x=\frac {1\pm \sqrt {1-4}}{2} $ has no solution so the are no answers that will satisfied all three. – fleablood Nov 17 '16 at 07:24