According to the fundamental theorem of algebra, how many zeros does the polynomial below have?

Question

asked Sep 4, 2019 80.9k views

2 Answers

Molokoloco · Answer 1 · 2019-09-08T03:57:21+0000

The given polynomial has 4 roots.

( may not be all distinct)

Fundamental Theorem of Algebra --

It states that every non-constant polynomial of degree n has exactly n roots counting multiplicity.

i.e. the roots may repeat.

i.e. the number of roots of a non-constant polynomial of degree n has atmost n distinct roots.

We are given a polynomial as:

f(x)=x^4+5x^3+10x^2+20x+24

Clearly the polynomial is of degree 4.

This means that the roots of this polynomial will be: 4

( not all roots may be distinct)