This document discusses classifying and finding the roots of quadratic equations. It reviews using the discriminant to determine if there are two real roots, a double root, or two complex roots. It then works through classifying and finding the roots of the equation x^2 + 2x + 1 = 0. It calculates the discriminant is 0, indicating a double root. It factors the equation as (x+1)^2, showing the double root is x = -1.

1. In section 7-3 of your textbook, you reviewed the concept of a discriminant. You may need to
reference that section for the following problems. For each equation listed: find the discriminant;
classify the root(s) as 2 real (unequal) roots, 1 (double) root, or 2 imaginary conjugate roots; and
c) find the roots by factoring, completing the square, or utilizing the quadratic formula (hint: you
probably will not want to Find imaginary roots by factoring). x2 + 2x + 1 = 0 Circle the proper
classification: 2 real (unequal) roots 1 double root (2 equivalent roots) 2 imaginary conjugate
roots
Solution
D =vb2-4ac = v2^2-4 = 0 Thus, it has two coincident roots. Factorizing, it is (x+1)^2. Thus, the
coincident roots are x = -1.