SOLUTION: If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0. My answer is (-infty,0) u (1,4) u (4,infty) is this right. thanks again.

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Question 43596This question is from textbook Algebra and trigonometry with analytic geometry
: If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0. My answer is (-infty,0) u (1,4) u (4,infty) is this right. thanks again. This question is from textbook Algebra and trigonometry with analytic geometry

Found 2 solutions by psbhowmick, Nate:
Answer by psbhowmick(878) (Show Source):
You can put this solution on YOUR website!
So you are right!

For all real values of 'x', except when x = 4.
So, for f(x) to be greater than 0, .
This is possible if

1) Case I
both x > 0 and (x - 1) > 0 which implies x > 1 [as x > 1 automatically satisfy both the conditions]

2) Case II
both x < 0 and (x - 1) < 0 which implies x < 0 [as x < 0 automatically satisfy both the conditions]

So for f(x) > 0, either x > 1 [from Case I] or x < 0 [from Case II]; also x not equal to 4.
Hence, the answer is (-,0)U(1,4)U(4,).

Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!

All the values above the x-axis are your answers because is greater than zero.
Answer: