Question

If degree of the polynomial p(x) is n, then write the maximum number of zeroes.​

Answer 1

Answer:

If degree of the polynomial p(x) is n,then the maximum no. of zeroes will be n.

Step-by-step explanation:

For a polynomial of degree a, the maximum number of roots (zeros) are a.

Let a general polynomial of degree n be

p(x)=a

n

x

n

+a

n−1

x

n−1

+........+a

0

Then, p(x)=a

n

(x−x

1

)(x−x

2

).....(x−x

n

)

Here, the roots (zeros) can be real, imaginary or both depending on the polynomial.

Answer 2

The Fundamental Theorem of Algebra states that any polynomial of degree n has exactly n complex roots (including repeated roots). Therefore, the maximum number of zeroes a polynomial of degree n can have is n.

It's important to note that these roots can be real or complex numbers, and they may be repeated. For example, a polynomial of degree 3 may have 3 distinct roots, or it may have 2 distinct roots and one repeated root. However, the total number of roots (including repeated roots) will always be n.

In summary, the maximum number of zeroes a polynomial of degree n can have is n.

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