Find the zeroes of the given polynomials . p(x)=x^4-16

alesterp

alesterp

Answered question

2021-09-01

Find the zeroes of the given polynomials
p(x)=x416

Answer & Explanation

Velsenw

Velsenw

Skilled2021-09-02Added 91 answers

The polynomial is given as,
P(x):x416
The degree of the given polynomial is four.
Therefore, it will have at-most 4 zeroes.
Equate the polynomial to zero,
P(x)=0
x416=0
x442=0
(x2)2(4)2=0
Consider the algebraic identity,
a2b2=(a+b+(ab)
Substitute the values,
(x2+4)(x24)=0
((x2)(2i)2)(x222)=0
(x2i)(x+2i)(x2)(x+2)=0
x2i=0 or x+2i=0 or x2=0 or x+2=0
x=2i or x=2i or x=2 or x=2z
Thus, the zeroes of the given polynomial are 2i,2i,2,2

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