Question 464016
b² - 4ac is the discriminant

If b² - 4ac = 0, then there is one real number solution
If b² - 4ac < 0, then there are two imaginary number solutions
If b² - 4ac > 0, then there are two real number solutions


x² = 6x + 2
x² - 6x - 2 = 0 {subtracted 6x and 2 from both sides}
a = 1, b = -6, c = -2 


b² - 4ac {the discriminant}
= (-6)² - 4(1)(-2) {substituted into the discriminant}
= 36 + 8 {simplified}
= 44 {added}
44 > 0


There are two different real number solutions ,
however &#8730;44 is irrational, therefore there are
A.) Two different irrational solutions
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