SOLUTION: Solve the polynomial equation by factoring and then using the zero product principle. 3x to the 4th power minus 75x to the second power = 0.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the polynomial equation by factoring and then using the zero product principle. 3x to the 4th power minus 75x to the second power = 0.      Log On


   

Question 21699: Solve the polynomial equation by factoring and then using the zero product principle. 3x to the 4th power minus 75x to the second power = 0.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by factoring:
3x%5E4+-+75x%5E2+=+0 Factor out 3x^2
3x%5E2%28x%5E2+-+25%29+=+0 Apply the zero product principle.
3x%5E2+=+0 and/or x%5E2+-+25+=+0
If 3x%5E2+=+0 then, x = 0
If x%5E2+-+25+=+0 then, x%5E2+=+25 and x = +5 or x = -5
The roots are:
x = 0 A double root.
x = 5
x = -5
Here's what the graph looks like.
graph%28300%2C200%2C-7%2C7%2C-500%2C10%2C3x%5E4-75x%5E2%29