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)

p (a) = 0

. In this situation, we say $p(x) = 0$ is a polynomial equation, and

a

is a root of the polynomial.

Example:

Example:

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1. Introduction to value and zero of a polynomial