Using the Fundamental Theorem of Algebra, complete the following exercise. Show your work. Determine how many, what type, and find the roots for f(x)=x3−5x2−25x+125.

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Using the Fundamental Theorem of Algebra, complete the following exercise. Show your work.   Determine how many, what type, and find the roots for f(x)=x3−5x2−25x+125.

temnimam2 · Accepted Answer

Step 1   Fundamental Theorem of Algebra, states if f(x) is a polynomial of degree n, where n&amp;gt;0, then f has at least one zero in the complex number system.    The polynomial given to us is f(x)=x3−5x2−25x+125.  Step 2   the highest power of this polynomial is 3 so, there will be 3 roots to this polynomial.    now, by factorizing the polynomial we get  f(x)=(x−5)(x2−25)  f(x)=(x−5)(x−5)(x+5)  f(x)=(x−5)2(x+5)  therefore, we can see that the roots of the polynomial are real and the roots of the polynomial are x=5,−5    and the multiplicity of the roots x=−5 is 2

Karen Robbins · Accepted Answer

by grouping method:   f(x)=x3−5x2−25x+125.   =x2(x−5)−25(x−5)   f(x)=(x−5)(x2−25)=(x−5)(x−5)(x+5)   f(x)=(x−5)2(x+5)

karton · Accepted Answer

Given that the function f(x)=x3−5x2−25x+125 We have to find the roots of f(x) Let us try to factorize the function to find the roots We can group two by two and find out f(x)=x2(x−5)−25(x−5) =(x2−25)(x−5) =(x+5)(x−5)2 We find that the roots are -5,5,5 Or -5 with a multiplicity of 1 and 5 with a multiplicity of 2 are the roots of the equation

Using the Fundamental Theorem of Algebra, complete the following exercise.

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