Question : Zero of the zero polynomial is
a) 0
b) 1
c) Any real nymber
d) Not defined
Doubt by Ashira
Solution :
We know, zero polynomial is a type of constant polynomial in which constant term is itself a zero.
Proper Definition of Zero Polynomial
A zero polynomial is a polynomial in which all the coefficients are equal to zero.
Here are some examples of zero polynomials:
Example 1 : 0
Example 2 : 0x + 0
Example 3 : 0x2 + 0x + 0
Example 4 : 0x3 + 0x2 + 0x + 0
As you can see, all of these polynomials have all of their coefficients equal to 0. Therefore, they are all zero polynomials.
Basically, it is a polynomial that is always equal to 0, no matter what value is substituted for the variables. So, the zero of a zero polynomial could be any real number.
Hence, c) Any real number would be the correct option.
Addition Knowledge :
Degree of Zero Polynomial
The zero polynomial is the only polynomial that has an undefined degree. This is because the degree of a polynomial is the highest power of the variable that appears in the polynomial. Since the zero polynomial has no terms, it has no variable and therefore no highest power.