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Hello,The Answer Checker could not return an answer to this question:Find: the zeros Given: f(x)=x^4-1The answer I came up with was x=1, am I close?

Vince024

by Vince024 at February 15, 2010

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You can factor x^4 - 1 = 0.(x^2+1)(x+1)(x-1).Therefore, the zeros are -1 and 1.  (i, the square root of negative one isn't a real answer.)

Delta Delta February 15, 2010

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Hi Vince - Yes, you are about half way there! Remember, the zeroes are the solutions to the function when it crosses the x-axis (or simply, when the function equals zero).  If you have a graphing calculator, it will help you see where the function crosses the x-axis. Set your equation equal to zero and solve for x. Hint: Taking an even root of both sides of an equation results in TWO solutions. Hope this helps  

Steve204 Steve204 February 15, 2010

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x=1 is one of the roots of the function, but there's more than just that one! One key thing to remember is that the highest degree of a function equals the number of roots in the function. In this case, f(x) is a 4th degree, or quartic, function (the highest exponent value is ^4). That means there are four roots in the equation, but it doesn't necessarily mean they are all real roots!To find all the roots, you need to factor the function completely, and that may involve nonreal roots, or values of x where it is actually not an x-intercept. Hope this helps!

Azaler Azaler February 15, 2010

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