Write whether the following statements are true or false. Justify your answer. ’
Question:

Write whether the following statements are true or false. Justify your answer. ’

(i) A Binomial can have atmost two terms.

(ii) Every polynomial is a Binomial.

(iii) A binomial ipay have degree 5.

(iv) Zero of a polynomial is always 0.

(v) A polynomial cannot have more than one zero.

(vi) The degree of the sum of two polynomials each of degree 5 is always 5.

Solution:

(i) False, because a binomial has exactly two terms.

(ii) False, because every polynomial is not a binomial .

e.g., (a) 3x2 + 4x + 5 [polynomial but hot a binomial]

(b) 3x2 + 5 [polynomial and also a binomial]

(Hi) True, because a binomial is a polynomial whose degree is a whole number greater than equal to one. So, it may have degree 5.

(iv) False, because zero of a polynomial can be any real number e.g., p(x) = x – 2, then 2 is a zero of polynomial p(x).

(v) False, because a polynomial can have any number of zeroes. It depends upon the degree of the polynomial

e.g., p(x) = x2 -2, as degree pf p(x) is 2 ,so it has two degree, so it has two zeroes i.e., √2 and —√2.

(vi) False, because the sum of any two polynomials of same degree is not always same degree.

e.g., Let f(x) = x4 + 2 and g(x) = -x4 + 4x3 + 2x

∴ Sum of two polynomials,

f{x) + g(x) = x4 + 2 + (-x4 + 4x3 + 2x)

= 4x3 + 2x + 2 which is not a polynomial of degree 4.