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I want to know if there is any way of finding out whether a quadratic equation has ratonal roots or not.

nonuser
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user168942
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  • Well, for the equation $ax^2 + bx + c = 0$, as long as $a, b, c$ are all rational, it all comes down to whether $b^2-4ac$ is the square of a rational number or not. I don't think more can be said, really. – Arthur Jan 17 '18 at 12:59
  • If one considers only the integer coefficients quadratic equations, then one has https://en.wikipedia.org/wiki/Rational_root_theorem –  Jan 17 '18 at 14:23

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Using the quadratic formula, $x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$. This means that you have to check $b^2-4ac$ whether it is a square number to check if the roots are under the square root.

QuIcKmAtHs
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