Question

Write maximum number of zeroes for p(x) = x

3

+ 3x

2

– 3x + 1

Answer 1

Infinitely number of solutions

Answer 2

Answer:

Given polynomial has maximum 3 zeroes.

Step-by-step explanation:

We have the polynomial, $p(x)=x^{3}+3x^{2}-3x+1$.

It is required to find the maximum number of zeroes of the polynomial.

i.e. To find the roots of the equation $p(x)=0$

From the 'Fundamental Theorem of Algebra', which states that,

'Any polynomial with degree 'n' have 'n' number of roots'.

We get that,

As the given polynomial is of 'degree 3'. So, $p(x)=0$ will have 3 roots.

Hence, the given polynomial has maximum 3 zeroes.