Finding a Quadratic Polynomial from Given Zeroes

Video Explanation

Question

A quadratic polynomial, the sum of whose zeroes is \(0\) and one zero is \(3\), is:

(a) \(x^2 – 9\)    (b) \(x^2 + 9\)    (c) \(x^2 + 3\)    (d) \(x^2 – 3\)

Solution

Step 1: Find the Other Zero

Let the zeroes be \( \alpha \) and \( \beta \).

Given:

\[ \alpha + \beta = 0 \]

If one zero is \(3\), then the other zero must be:

\[ \beta = -3 \]

Step 2: Form the Quadratic Polynomial

A quadratic polynomial with zeroes \(3\) and \(-3\) is:

\[ (x – 3)(x + 3) \]

\[ = x^2 – 9 \]

Conclusion

The required quadratic polynomial is:

\[ \boxed{x^2 – 9} \]

Hence, the correct option is (a) \(x^2 – 9\).