Chapter 11 - Quadratic Functions and Equations - 11.3 Studying Solutions of Quadratic Equations - 11.3 Exercise Set - Page 718: 11

$2$ different irrational solutions that are conjugates.

$ x^{2}-11=0\qquad$.... $a=1,\ b=0,\ c=-11$ $ b^{2}-4ac\qquad$....substitute $b$ for $0,\ a$ for $1$ and $c$ for $-11$ $=(0)^{2}-4\cdot 1\cdot(-11)$ $=0+44$ $=44$ Since the discriminant is a positive number that is not a perfect square, there are $2$ different irrational solutions that are conjugates.