To find: the real zeros of polynomial function form an arithmetic sequaence f(x)=x^{4}-4x^{3}-4x^{2}+16x

FobelloE

FobelloE

Answered question

2021-08-07

To find:
The real zeros of polynomial function form an arithmetic sequaence
f(x)=x44x34x2+16x

Answer & Explanation

davonliefI

davonliefI

Skilled2021-08-08Added 79 answers

A ration expression is a fraction that is quotient of two polynomials. A rational function is defined by the two polynomial functions.
A function f of the form f(x)=p(x)q(x) is a rational function.
Where, p(x) and q(x) are polynomial functions, with q(x)q0.
Calculation:
The given polinomial function form an arithmetic sequence is
f(x)=x44x34x2+16x
Here, the constant is 0.
The above equatioon can be rewritten as
f(x)=x(x34x24x+16)
The possiblities for pq are ±1, ±2, ±4 and ±8
Factoring the term (x34x24x+16), we get
(x34x24x+16)=(x+2)(x26x+8)
Factoring the term (x26x+8), we get
(x26x+8)=(x2)(x4)
Combining all the terms, we get
(x34x24x+16)=(x+2)(x2)(x4)
So, f(x)=x(x34x24x+16)=x(x+2)(x2)(x4)
Thus, the real zeros are 2, 0, 2, and 4.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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