SOLUTION: use the discriminant to determine whether the following equations have solutions that are: two different rational solutions;two different irrational solutions;exactly one rational

Question 335952: 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:

could someone please help me with this problem?
thank you
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Get every term to the left side.

Combine and rearrange the terms.

From we can see that , , and

Start with the discriminant formula.

Plug in , , and

Square to get

Multiply to get

Rewrite as

Add to to get

So the discriminant is

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

So the answer is "two different irrational solutions"

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim

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