ZERO OF A POLYNOMIAL
2.3 Zero of a polynomial p(x) is a number ‘a ‘such that p(a) = 0
Consider the polynomial p(x) = x – 4
P (4) = 4 – 4 = 0
: We say that 4 is a zero of the polynomial p(x)
Zero of the polynomial is also called the root of the polynomial
Finding the zeroes means solving the equation p(x) = 0
A polynomial can have more than one zero, but linear polynomial will have only one zero
EXERCISE 2.2
1. Find the value of the polynomial (x) = 5x − 4×2 + 3for
(i) x = 0 (ii) x = – 1 (iii) x = 2
Solution:
(i) p (x) = 5x – 4×2 + 3 for x = 0
In place of x put 0
p (0) = 5(0) – 4 (0)2 + 3
= 0 – 0 + 3
p (0) = 3
5x – 4 x 2 + 3 for x = 0 is 3
2. Find p(0), p(1) and p(2) for each of the following polynomials:
Solution:
3. Verify whether the following are zeroes of the polynomial, indicated against them.
Solution:
4. Find the zero of the polynomials in each of the following cases:
Solution:
