SOLUTION: How do we determine the number of real roots of an equation? can you determine the number of real solutions in the following equations? 1. x^2 - 5x = 0 2. x^2 + 2x + 8

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: How do we determine the number of real roots of an equation? can you determine the number of real solutions in the following equations? 1. x^2 - 5x = 0 2. x^2 + 2x + 8      Log On


   

Question 423756: How do we determine the number of real roots of an equation?
can you determine the number of real solutions in the following equations?
1. x^2 - 5x = 0
2. x^2 + 2x + 8 = 0

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


From x%5E2-5x we can see that a=1, b=-5, and c=0


D=b%5E2-4ac Start with the discriminant formula.


D=%28-5%29%5E2-4%281%29%280%29 Plug in a=1, b=-5, and c=0


D=25-4%281%29%280%29 Square -5 to get 25


D=25-0 Multiply 4%281%29%280%29 to get %284%29%280%29=0


D=25 Subtract 0 from 25 to get 25


So the discriminant is D=25


Since the discriminant is greater than zero, this means that there are two real solutions.

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# 2

From x%5E2%2B2x%2B8 we can see that a=1, b=2, and c=8


D=b%5E2-4ac Start with the discriminant formula.


D=%282%29%5E2-4%281%29%288%29 Plug in a=1, b=2, and c=8


D=4-4%281%29%288%29 Square 2 to get 4


D=4-32 Multiply 4%281%29%288%29 to get %284%29%288%29=32


D=-28 Subtract 32 from 4 to get -28


So the discriminant is D=-28


Since the discriminant is less than zero, this means that there are two complex solutions.


In other words, there are no real solutions.


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