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)

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.

Did you find an error?

2. Zeroes of a polynomial