# Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 80

There are two identical real solutions.

#### Work Step by Step

$4x^{2}+12x+9=0$ To determine the nature of the solutions (without solving), we compute the sign of the discriminant in the quadratic formula ($a=4,\ b=12,\ c=9$): $b^{2}-4ac=12^{2}-4*4*9=144-144=0$ Since the discriminant is 0, there are two identical real solutions.

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