a) Find the rational zeros and then the other zeros of the polynomial function displaystyle{left({x}right)}={x}^{3}-{4}{x}^{2}+{2}{x}+{4},

Zoe Oneal

Zoe Oneal

Answered question

2021-01-02

a) Find the rational zeros and then the other zeros of the polynomial function (x)=x34x2+2x+4,that is, solve f(x)=0.
b) Factor f(x) into linear factors.

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-01-03Added 95 answers

Step 1
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.
Step 2
Then we use x=2 to find the other factor. We use synthetic division.
image
Another factor is x22x2.
Step 3
Then we use the quadratic formula to find the zeros fromit
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
Step 4
b) Linear factored form of f is:
f(x)=[x(13)](x2)[x(1+3)]
f(x)=(x1+3)(x2)(x13)
Answer: (x1+3)(x2)(x13)

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