SOLUTION: I am stuck on correct answer for: (y^2 - 4y + 3) - (4y^2 + 5Y - 2) = I am not using any specific book. I am just practicing...

Algebra ->  Square-cubic-other-roots -> SOLUTION: I am stuck on correct answer for: (y^2 - 4y + 3) - (4y^2 + 5Y - 2) = I am not using any specific book. I am just practicing...      Log On


   

Question 54498: I am stuck on correct answer for:
(y^2 - 4y + 3) - (4y^2 + 5Y - 2) =

I am not using any specific book. I am just practicing...
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
y^2 - 4y + 3 - 4y^2 - 5y + 2
-3y^2 - 9y + 5
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case -3y%5E2%2B-9y%2B5+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-9%29%5E2-4%2A-3%2A5=141.

Discriminant d=141 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+141+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+141+%29%29%2F2%5C-3+=+-3.47905701450632
y%5B2%5D+=+%28-%28-9%29-sqrt%28+141+%29%29%2F2%5C-3+=+0.479057014506319

Quadratic expression -3y%5E2%2B-9y%2B5 can be factored:
-3y%5E2%2B-9y%2B5+=+-3%28y--3.47905701450632%29%2A%28y-0.479057014506319%29
Again, the answer is: -3.47905701450632, 0.479057014506319. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B-9%2Ax%2B5+%29