Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. Find the real zeros of f(x) = 5x^{3} - x^{2} + 5x - 1

waigaK 2021-02-21 Answered
Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
Find the real zeros of f(x)=5x3  x2 + 5x  1
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AGRFTr
Answered 2021-02-22 Author has 95 answers

Given: find all real zeros of f(x)=5x3  x2 + 5x  1, and use the zeros to factor f over the real numbers.
Used concept :
Rational zeros theorem:
Let P(x) is a polynomial. if p/q isazetoof P(x) then p is the factor of the constant term of P(x) and q is the factor of the leading coefficient of P(x).
Let pq is the rational zero of the given polynomial.
Here, p is a factor of the constant term 1
and q is a factor of the leading coefficient 5.
So, the possible value of p= ± 1
and g=  1,  15
Now, the possible value of pq=  1,  15
Now, check the value of function
f(x)=5x3  x2 + 5x  1
f(1)=5(1)3  (1)2 + 5 1=8  0
f(1)=5(1)3  (1)2 + 5(1)  1= 12  0
f(15)=5(13)3  (15)2 + 5(15)  1=0
f(15)=5(15)3  (15)2 + 5(15)  1= 5252  0
So, the zero of the given function is 15 in real numbers.
f(x)=5x3  x2 + 5x  1
f(x)=x2(5x  1) + 1(5x  1)
f(x)=(5x  1)(x2 + 1)
Finally answer is:
(5x  1)(x2 + 1)

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Jeffrey Jordon
Answered 2021-11-03 Author has 2047 answers

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