Any algebraic expression which includes variable which have only positive powers are called Polynomials. We must remember that algebraic expression is always separated by the '+' or '–' operators, which we call terms of expression.
There exist a difference between zero polynomial and the zero of the polynomial. By zero polynomial we Mean that polynomial has only one term, namely zero only.
Before learning about zero of polynomial, let us first learn how to find the value of polynomial at a given Point. If p(x) is a polynomial in 'x' and 'α' is any of real number, then if we put value of x = α in the polynomial p(x), so that polynomial becomes p (α), then value so obtained by putting value of x = α.
Now we will learn Finding Zeroes of Polynomials. If we have a polynomial P(x), then we say that 'α' is called zero of polynomial p (x) if we find that p (α) = 0. Thus we say that on putting value of x = α, if value of polynomial becomes zero, then we say that 'α' is zero of the polynomial.
Let us assume p (x)= x2 – 2x - 3, then find p (3),
Sol: Here by putting value of x = 3 in the polynomial p(x)= x2 – 2x - 3, we will get:
P(3) = 32 – 2 * 3 – 3
= 3 * 3 – 6 – 3
= 9 – 6 – 3
= 9 – 9 = 0
So we observe that polynomial p (x) is zero at point x = 3, thus we say that value 3 is zero of polynomial. Similarly at x = -1, p(x) = 0, so zeros of polynomial are 3 and -1.