Find all the real and complex zeros of the following polynomials.f(x)=x^4-4x^3+7^2-16x +12

Maiclubk

Maiclubk

Answered question

2021-09-15

Find all the real and complex zeros of the following polynomials.
f(x)=x44x3+7216x+12

Answer & Explanation

Neelam Wainwright

Neelam Wainwright

Skilled2021-09-16Added 102 answers

It is given that, f(x)=x44x3+7216x+12
We have to find all the real and complex zeros of the polynomial.
We have, f(x)=x44x3+7x216x+12
For the zeros of polynomial,
x44x3+7x216x+12=0
(x3)(x3x2+4x4)=0
(x3)(x1)(x2+4)=0
(x3)=0 or (x1)=0 or (x2+4)=0
x=3 or x=1 or x2=4
x=3 or x=1 or x=±2i
There are four zeros of the polynomial
Two real numbern x=1,3
Two complex number =2i,2i

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