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

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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:
10-5a%5E2=7a%2B9
could someone please help me with this problem?
thank you
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
10-5a%5E2=7a%2B9 Start with the given equation.


10-5a%5E2-7a-9=0 Get every term to the left side.


-5a%5E2-7a%2B1=0 Combine and rearrange the terms.


From -5a%5E2-7a%2B1 we can see that a=-5, b=-7, and c=1


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


D=%28-7%29%5E2-4%28-5%29%281%29 Plug in a=-5, b=-7, and c=1


D=49-4%28-5%29%281%29 Square -7 to get 49


D=49--20 Multiply 4%28-5%29%281%29 to get %28-20%29%281%29=-20


D=49%2B20 Rewrite D=49--20 as D=49%2B20


D=69 Add 49 to 20 to get 69


So the discriminant is D=69


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