Abstract Algebra: Theory and Applications · Problem 17.6.1

Integral Domains — Thomas Judson

Mathematics — Abstract Algebra · solving-quadratic

Problem

Complete the square to solve the general quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 to obtain x=−b±b2−4ac2a.x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. The discriminant of the quadratic equation Δ=b2−4ac\Delta = b^2 - 4ac determines the nature of the solutions of the equation. If Δ>0\Delta > 0, the equation has two distinct real solutions. If Δ=0\Delta = 0, the equation has a single repeated real root. If Δ<0\Delta < 0, there are two distinct imaginary solutions.

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