SOLUTION: Solve the following equation. 1/5 r^(3/2) + 5/2 r^(1/2) =0. Thanks a lot!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the following equation. 1/5 r^(3/2) + 5/2 r^(1/2) =0. Thanks a lot!      Log On


   

Question 1051558: Solve the following equation.
1/5 r^(3/2) + 5/2 r^(1/2) =0. Thanks a lot!
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F5%29%2Ar%5E%283%2F2%29%2B%285%2F2%29%2Ar%5E%281%2F2%29=0
%282%29%2Ar%5E%283%2F2%29%2B%2825%29%2Ar%5E%281%2F2%29=0
%282%29%2AS%5E%283%29%2B%2825%29%2AS=0
S%28%282%29%2AS%5E%282%29%2B%2825%29%29=0
first case s=0 meaning r=0
%282%29%2AS%5E%282%29%2B%2825%29=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aS%5E2%2BbS%2Bc=0 (in our case 2S%5E2%2B0S%2B25+=+0) has the following solutons:

S%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=%280%29%5E2-4%2A2%2A25=-200.

The discriminant -200 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -200 is + or - sqrt%28+200%29+=+14.142135623731.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B0%2Ax%2B25+%29