SOLUTION: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rationa
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Question 464016: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x^2 = 6x + 2
a) Two different irrational solutions
b) Exactly one rational solution
c) Two different rational solutions
d) Two different imaginary solutions
Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
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 √44 is irrational, therefore there are
A.) Two different irrational solutions
For more help from me, visit: www.algebrahouse.com
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