Using the Discriminant
Date: 07/19/2000 at 00:34:33 From: Kemy Subject: Character of a solution in the complex numbers system Hi: I was asked to determine the character of the solution of the equation: x^2 + 2x + 6 = 0 in the complex number system without solving. How can I do that?
Date: 07/19/2000 at 11:37:55 From: Doctor Rob Subject: Character of a solution in the complex numbers system Thanks for writing to Ask Dr. Math, Kemy. For the equation a*x^2 + b*x + c = 0, assuming a, b, and c are real numbers, you can tell the character of the roots by examining b^2 - 4*a*c, which is called the "discriminant" of the equation. If this is negative, then the roots are complex numbers. If this is zero, there are two equal real roots. If this is positive, there are two unequal real roots. Furthermore, if a, b, and c are rational numbers, then the solutions in this last case will be rational if and only if the discriminant is a perfect square of a rational number. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/
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