# What is the number of zeros of the ‘zero polynomial’?

(a). 0

(b). 1

(c). 2

(d). Infinite

Last updated date: 20th Mar 2023

•

Total views: 304.5k

•

Views today: 7.82k

Answer

Verified

304.5k+ views

Hint: Recall the definition for zero polynomial and zeros of a polynomial and determine the number of roots of the zero polynomial.

Complete step-by-step answer:

A polynomial is an expression consisting of variables raised to some exponents along with their coefficients. It involves only the operations of addition, subtraction, multiplication, and not negative integer exponentiation. Examples of a polynomial are 5x, \[6{x^2} + 5\] and so on.

Zero polynomial is the constant polynomial whose coefficients are all equal to 0, hence, it’s name. It is a constant function with value zero and it takes all values of x to a single value, that is, zero. It is also the additive identity of the group of polynomials, since any polynomial added to zero polynomial gives back the same polynomial.

The zero polynomial is represented as follows:

P(x) = 0

We know that the zeros of any polynomial is the value of x for which the value of the polynomial becomes zero. For example, the zero of the polynomial p(x) = x – 1 is x = 1, since, for the value of x equal to 1, the value of the polynomial becomes 0.

We see that for the zero polynomial, P(x) = 0, any value of x, will give the value of P(x) to be zero.

Hence, the number of zeros of the polynomial is infinite.

Hence, option (d) is the correct answer.

Note: You might wrongly select option (a), thinking that the degree of the polynomial is zero, hence, it has zero solution. Yes, it is true the number of zeros is equal to the degree but zero polynomial is special and its value itself is equal to zero.

Complete step-by-step answer:

A polynomial is an expression consisting of variables raised to some exponents along with their coefficients. It involves only the operations of addition, subtraction, multiplication, and not negative integer exponentiation. Examples of a polynomial are 5x, \[6{x^2} + 5\] and so on.

Zero polynomial is the constant polynomial whose coefficients are all equal to 0, hence, it’s name. It is a constant function with value zero and it takes all values of x to a single value, that is, zero. It is also the additive identity of the group of polynomials, since any polynomial added to zero polynomial gives back the same polynomial.

The zero polynomial is represented as follows:

P(x) = 0

We know that the zeros of any polynomial is the value of x for which the value of the polynomial becomes zero. For example, the zero of the polynomial p(x) = x – 1 is x = 1, since, for the value of x equal to 1, the value of the polynomial becomes 0.

We see that for the zero polynomial, P(x) = 0, any value of x, will give the value of P(x) to be zero.

Hence, the number of zeros of the polynomial is infinite.

Hence, option (d) is the correct answer.

Note: You might wrongly select option (a), thinking that the degree of the polynomial is zero, hence, it has zero solution. Yes, it is true the number of zeros is equal to the degree but zero polynomial is special and its value itself is equal to zero.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE