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

Question 281671: 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.
x2 + 10x + 19 = 0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

From we can see that , , and

Start with the discriminant formula.

Plug in , , and

Square to get

Multiply to get

Subtract from to get

Since the discriminant is greater than zero, and isn't a perfect square, this means that there are two real and irrational solutions.

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