SOLUTION: p+(1/4)*p^(1/2)+K^2=0, What is the value of k to make perfect square...?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: p+(1/4)*p^(1/2)+K^2=0, What is the value of k to make perfect square...?      Log On


   

Question 979430: p+(1/4)*p^(1/2)+K^2=0, What is the value of k to make perfect square...?
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
p%2B%281%2F4%29%2Ap%5E%281%2F2%29%2BK%5E2=0
=> p%2BK%5E2=-%281%2F4%29%2Ap%5E%281%2F2%29
=> 4p%2B4K%5E2+=+-p%5E%281%2F2%29
Squaring both sides,
16p%5E2%2B16K%5E4%2B32pk%5E2+=+p
=> 16p%5E2%2B%2832K%5E2-1%29p%2B16K%5E4+=+0
For perfect square, Discriminant=0
%2832K%5E2-1%29%5E2-4%2A16%2A16K%5E4+=+0
=>1024K%5E4-64K%5E2%2B1-1024K%5E4=0
=> K%5E2=+1%2F64
=> K=1%2F8