(a) find the rational zeros and then the other zeros of the polynomial function (x)=x3-4x2+2x+4, that is, solve f(x)=0. (type an exact answer, using r

Dottie Parra

Dottie Parra

Answered question

2020-12-24

(a) find the rational zeros and then the other zeros of the polynomial function (x)=x34x2+2x+4, that is, solve
f(x)=0. (type an exact answer, using radicals as needed. Simplify your answer. Use a comma to separate answers as needed.)
(b) Factor f(x) into linear factors. (type an exact answer, using radicals as needed. Simplify your answer. Type an expression using x as the variable.)

Answer & Explanation

SoosteethicU

SoosteethicU

Skilled2020-12-25Added 102 answers

a) We graph f(x)=x34x2+2x+4 using a graphing calculator to find the rational zeros.
image
It cuts the graph at x=2
Means x=2 is a zero.
Then we use x=2 to find the other factor. We use synthetic division.
Another factor is x22x2.
Then we use the quadratic formula to find the zeros from it
x22x2=0
x=2±(2)24(1)(2)2(1)
x=2±122
x=2±232
x=1±3
Answer (a):13,2,1+3
image
b) Linear factored form of f is:
image
Answer: (x1+3)(x2)(x13)

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