The number of polynomials having zeroes as -2 and 5 is

Options

A. 1
B. 2
C. 3
D. more than 3

Explanation

To find the number of polynomials having zeroes as -2 and 5, let's follow these steps:

### Step-by-Step Solution:

1. **Identify the zeroes of the polynomial:**
Given zeroes are \(\alpha = -2\) and \(\beta = 5\).

2. **Form the polynomial using the zeroes:**
The general form of a quadratic polynomial with zeroes \(\alpha\) and \(\beta\) is:
\[ f(x) = k(x - \alpha)(x - \beta) \]
where \(k\) is a constant.

3. **Substitute the given zeroes:**
Substitute \(\alpha = -2\) and \(\beta = 5\) into the polynomial:
\[ f(x) = k(x + 2)(x - 5) \]

4. **Expand the polynomial:**
Expand the expression \((x + 2)(x - 5)\):
\[ (x + 2)(x - 5) = x^2 - 5x + 2x - 10 = x^2 - 3x - 10 \]
So, the polynomial becomes:
\[ f(x) = k(x^2 - 3x - 10) \]

5. **Determine the number of possible polynomials:**
Since \(k\) can be any non-zero constant, there are infinitely many polynomials that can be formed by multiplying \(x^2 - 3x - 10\) by different constants.

### Conclusion:
The number of polynomials having zeroes as -2 and 5 is infinite.