SOLUTION: To find zeros of the fn. - x^4 - x^3 - 4x^2 + 4 step by step (not on calculator). Thanks

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Question 888096: To find zeros of the fn. -
x^4 - x^3 - 4x^2 + 4
step by step (not on calculator).
Thanks
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Set the expression equal to zero. Factor and solve.

x^4 - x^3 - 4x^2 + 4 = 0

(x^4 - x^3) + (-4x^2 + 4) = 0

x^3(x - 1) + (-4x^2 + 4) = 0

x^3(x - 1) -4(x^2 - 1) = 0

x^3(x - 1) -4(x - 1)(x + 1) = 0

x^3(x - 1) -4(x + 1)(x - 1) = 0

(x^3 - 4(x+1))(x - 1) = 0

Then you use the zero product property to get these two equations

x^3 - 4(x+1) = 0 or x-1=0

The first equation x^3 - 4(x+1) = 0 needs a calculator because this is a cubic (most cubics are nearly impossible to solve by hand)

The approximate solution to x^3 - 4(x+1)=0 is x = 2.382975768

The solution to x-1 = 0 is x = 1

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So the two real number solutions are

x = 1 or x = 2.382975768