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 460102: 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
8x^2 + 7x + 3 = 0
Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
From 8x%5E2%2B7x%2B3 we can see that a=8, b=7, and c=3


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


D=%287%29%5E2-4%288%29%283%29 Plug in a=8, b=7, and c=3


D=49-4%288%29%283%29 Square 7 to get 49


D=49-96 Multiply 4%288%29%283%29 to get %2832%29%283%29=96


D=-47 Subtract 96 from 49 to get -47


So the discriminant is D=-47


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


In other words, there are no real solutions.