Introduction to value and zero of a polynomial — lesson. Mathematics State Board, Class 9.

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The value of the polynomial

$p(x)$ at

$x=a$ is

$p(a)$ acquired when

$x$ is replaced by

$a$ (

$a∈R$ ).

Example:

Write the value of

$p(x) = x^2+2x-1$ at

$x = 3$ .

The value of

$p(x)$ at

$x = 3$ can be obtained by substituting the point

$x = 3$ in the polynomial.

Substitute

$x=3$ in the polynomial

$p(x)$ .

$p(3) =$

$3^2+2(3)-1$

$=9+6-1$

$=14$ .

Zero of polynomial

$p(x)$ is a real number '

$a$ ' such that

$p(a)= 0$ .

For polynomial

$p(x)$ , if

$p(a) = 0$ then the zero polynomial is

$x = a$ .

So, we put

$p(x) = 0$ to find zero polynomial.

The value of

$x$ is then found.

Important!

1. Zero of a polynomial: To find the zero of polynomial, we put

$p(x) =$

$0$ in the given polynomial

$p(x)$ .

Example:

2. Zeros of a polynomial

$p (x)$ is the real number '

$a$ ' for which

$p (x)$ if

$p (a) = 0$ . In this situation, we say

$p(x) = 0$ is a polynomial equation, and

$a$ is a root of the polynomial.

Each real number is a zero of the zero polynomial $p (x) = 0$ .

Example:

The non -zero constant polynomial does not have zeros.

Example:

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1. Introduction to value and zero of a polynomial

Theory: