Zeroes of a polynomial — lesson. Mathematics CBSE, Class 9.

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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 of the polynomial is

$x = a$ .

So, we put

$p(x) = 0$ to find zero of the 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

$p(x)$ .

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.

3. Each real number is a zero of the zero polynomial

$p (x) = 0$ .

4. The non-zero constant polynomial does not have zeros.

Example:

1. Find the zero of the polynomial

$p(x)=3a$ .

Putting

$p(x) = 0$ in the polynomial equation.

$\begin{array}{l} 0 = 3 a . \\ 0 / 3 = a \\ 0 = a \end{array}$

Thus,

$a=0$ is the zero of the polynomial

$p(a)=3a$ .

2. Find the zero of a polynomial

$p (x) = x - 2$ .

Putting

$p(x) = 0$ in the polynomial equation.

$\begin{array}{l} 0 = x - 2 \\ x = 2 \end{array}$

Thus

$x=2$ is the zero of the polynomial

$p (x) = x - 2$ .

3. For the zero polynomial,

$p(8) = 0$ ,

$8$ is the zero and it is a real number.

4. For the constant polynomial

$p (x) = 8$ does not have a zero.

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2. Zeroes of a polynomial

Theory: