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find the real zeros of the following function f(x)=x^3-5x^2+5x-1

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I  need to figure this out for Alegbra II.

asked Nov 23, 2013 in ALGEBRA 2 by chrisgirl Apprentice

1 Answer

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Identify Rational Zeros  

Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

f (x )=  x3- 5x2+ 5x - 1

If p/q is a rational zero, then p is a factor of and q  is a factor of 1.

The possible values of p are   ± 1.

The possible values for q  are ± 1.

So, p /q = ± 1

Make a table for the synthetic division and test possible  zeros.

p /q 1 -5 5 -1
1 1 -6 11 -12
1 1 -4 1 0

Since f (1) = 0,   x  = 1 is a zero. The depressed polynomial is x2- 4x + 1 = 0

Since the depressed polynomial of this zero, x2- 4x + 1, is quadratic, use the Quadratic Formula to find the roots of the related quadratic equation x2- 4x + 1 = 0

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Roots are

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Zeros of function image

Real zero of function f (x) = x3- 5x2+ 5x - 1 is at x  = 1.

answered Aug 12, 2014 by david Expert

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