SOLUTION: Please help me !! Solve. Identify all double roots. a) 8y^2 +1 = 6y b) x^4-25x^2 =0 c)(X-3)^3-(x-3)^2= 0 PLEASE HELP!!!!!

Algebra ->  Equations -> SOLUTION: Please help me !! Solve. Identify all double roots. a) 8y^2 +1 = 6y b) x^4-25x^2 =0 c)(X-3)^3-(x-3)^2= 0 PLEASE HELP!!!!!      Log On


   

Question 87489: Please help me !!
Solve. Identify all double roots.
a) 8y^2 +1 = 6y
b) x^4-25x^2 =0
c)(X-3)^3-(x-3)^2= 0
PLEASE HELP!!!!!
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
A double root occurs when the power of the factor that gives you the root is 2.

a) 8y^2 +1 = 6y
8y%5E2+-+6y+%2B1%29+=+0
%284y-1%29%282y-1%29=0
No double roots, since the powers of the factors are not 2.

b) x^4-25x^2 =0
x%5E2%28x%5E2+-25%29+=+0
x%5E2%28x-5%29%28x%2B5%29+=+0
x=0 is of multiplicity 2, since the power of the x factor is 2.

c)(X-3)^3-(x-3)^2= 0
%28x-3%29%5E2%28x-3+-+1%29+=+0
%28x-3%29%5E2%28x-4%29+=+0
x=3 is of multiplicity 2, since the power of the (x-3) factor is 2.

R^2 Retired from SCC