Find all the zeros of the polynomial: f(x)=x^{3}+4x^{2}-41x+36 ... if (x-4) is

klytamnestra9a

klytamnestra9a

Answered question

2021-12-03

Find all the zeros of the polynomial:
f(x)=x3+4x241x+36
... if (x-4) is a factor of this polynomial.

Answer & Explanation

Otigh1979

Otigh1979

Beginner2021-12-04Added 17 answers

Step 1
Given,
f(x)=x3+4x241x+36
(x-4) is a factor of this polynomial
We have to find the all the zeros of the polynomial.
Step 2
We have
f(x)=x3+4x241x+36
(x-4) is a factor of this polynomial
So,
Factorizing f(x)=x3+4x241x+36 further
x3+4x241x+36
x34x2+8x232x9x+36
x2(x4)+8x(x4)9(x4)
(x4)(x2+8x9)
(x4)(x2+9xx9)
(x4)(x(x+9)1(x+9))
(x4)(x+9)(x1)
Step 3
Now,
For finding the zeros of the f(x)
Then,
f(x)=0
(x4)(x1)(x+9)=0
x-4=0 or x-1=0 or x+9=0
x=4 or x=1 or x=-9
So,
The zhe zeros the of f(x) is x = 4, 1 and -9 Answer

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