SOLUTION: Someone please help. y^2=5/7y+3/7 Does it have 2 non-real solutions, 2 real solutions, or 1 real solutions. Thank you.

Algebra ->  Equations -> SOLUTION: Someone please help. y^2=5/7y+3/7 Does it have 2 non-real solutions, 2 real solutions, or 1 real solutions. Thank you.      Log On


   

Question 132299: Someone please help.
y^2=5/7y+3/7 Does it have 2 non-real solutions, 2 real solutions, or 1 real solutions.
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2=%285%2F7%29y%2B3%2F7 Start with the given equation


0=%285%2F7%29y%2B3%2F7-y%5E2 Subtract y%5E2 from both sides


0=-y%5E2%2B%285%2F7%29y%2B3%2F7 Rearrange the terms


7%2A0=7%28-y%5E2%2B%285%2F7%29y%2B3%2F7%29 Multiply both sides by the LCD 7. This will eliminate the fractions


0=-7y%5E2%2B5y%2B3 Distribute and multiply


From the quadratic formula

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

the discriminant consists of all of the terms in the square root. So the discriminant is

D=b%5E2-4ac

the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.


Now let's find the discriminant for y=-7y%5E2%2B5y%2B3:

D=b%5E2-4ac Start with the given equation

D=%285%29%5E2-4%2A-7%2A3 Plug in a=-7, b=5, c=3

D=25-4%2A-7%2A3 Square 5 to get 25

D=25%2B84 Multiply -4*-7*3 to get 84

D=109 Combine 25 and 84 to get 109


Since the discriminant equals 109 (which is greater than zero) , this means there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.