Question

Write whether the following statements are true or false. Justify your answer. ’ -Maths 9th

Answer 1

(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.