Mathematics: if its a triangle then i has 3 sides what kind of statmente?

if its a triangle then i has 3 sides what kind

chandlerstandi8294

11.06.2020

The polynomial function is given by:

f(x)=x^4-3x^2-4

Step-by-step explanation:

We are given the roots of a polynomial function as:

i, –2, and 2.

Also, the leading coefficient is: 1

We know that if for any polynomial function the complex number is a root of the polynomial then it's conjugate is also a root of the function.

i.e. here i is a root.

Hence, -i is also a root of the polynomial function.

The function will be given by:

$f(x)=(x-2)(x+2)(x-i)(x+i)\\\\i.e.\\\\f(x)=(x^2-4)(x^2-i^2)$

Since, we know that:

(a+b)(a-b)=a^2-b^2

Hence, we have:

f(x)=(x^2-4)(x^2+1)

( since,

i^2=-1 )

Hence, we have:

$f(x)=x^2(x^2+1)-4(x^2+1)\\\\i.e.\\\\f(x)=x^4+x^2-4x^2-4\\\\i.e.\\\\f(x)=x^4-3x^2-4$

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