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 209761: 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.
v2 - 6v - 2 = 0
A) Two different irrational solutions
B) Exactly one rational solution
C) Two different rational solutions
D) Two different imaginary solutions
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

Rewrite as

Add to to get

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 square root of 44 will be irrational. So this means that you will have two different irrational (and real) solutions.

So the answer is A)
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