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 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) About Me  (Show Source):
You can put this solution on YOUR website!

From v%5E2-6v-2 we can see that a=1, b=-6, and c=-2


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


D=%28-6%29%5E2-4%281%29%28-2%29 Plug in a=1, b=-6, and c=-2


D=36-4%281%29%28-2%29 Square -6 to get 36


D=36--8 Multiply 4%281%29%28-2%29 to get %284%29%28-2%29=-8


D=36%2B8 Rewrite D=36--8 as D=36%2B8


D=44 Add 36 to 8 to get 44


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)