real numbers and a . Now consider the polynomial p ( x ) = x – x – . Then, putting x = in the polynomial, we get p ( ) = – × – = – . The value ‘– ’, obtained by replacing x by in x – x – , is the value of x – x – at x = .
Similarly, p ( ) is the value of p ( x ) at x = , which is – . If p ( x ) is a polynomial in x , and if k is any real number, then the value obtained by replacing x by k in p ( x ), is called the value of p ( x ) at x = k , and is denoted by p ( k ). What is the value of p ( x ) = x – x – at x = – ? We have : p (– ) = (– ) –{ × (– )} – = Also, note that p ( ) = – ( ) – = .
As p (– ) = and p ( ) = , – and are called the zeroes of the quadratic polynomial x – x – . More generally, a real number k is said to be a zero of a polynomial p ( x ) , if p ( k ) = . You have already studied in Class IX, how to find the zeroes of a linear polynomial. For example, if k is a zero of p ( x ) = x + , then p ( k ) = gives us k + = , i.e., k = In general, if k is a zero of p ( x ) = ax + b , then p ( k ) = ak + b = , i.e., k So, the zero of the linear polynomial ax + b is