SOLUTION: How do you solve for x in the following equation: (2*x^6)*((x-4)^2)*((x-1)^2)=0

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Question 65063: How do you solve for x in the following equation: (2*x^6)*((x-4)^2)*((x-1)^2)=0
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve for x in the following equation: (2*x^6)*((x-4)^2)*((x-1)^2)=0
The zero product property says that we can set each factor = to 0 and solve for x.
2x^6=0
(2x^6)/2=0/2
x^6=0
6th root (x^6)= 6th root (0)
highlight%28x=0%29
(x-4)^2=0
sqrt(x-4)^2=sqrt(0)
x-4=0
x-4+4=0+4
highlight%28x=4%29
(x-1)^2=0
sqrt(x-1)^2=sqrt(0)
x-1=0
x-1+1=0+1
highlight%28x=1%29
Therefore the solution set for x is x={0,1,4}
Check if you let x= 0,1, or 4 both sides of the equation will =0 because 0 times anything is 0.
Happy Calculating!!!