Quadratic Polynomial with Sum and Product of Zeroes
To find the quadratic polynomial with the given sum and product of its zeroes, we can use the following key points:

Key Points:
- The sum of the zeroes of a quadratic polynomial \( ax^2 + bx + c \) is given by \( \frac{-b}{a} \).
- The product of the zeroes of a quadratic polynomial \( ax^2 + bx + c \) is given by \( \frac{c}{a} \).

Given Information:
Sum of the zeroes = -5
Product of the zeroes = 6

Finding the Quadratic Polynomial:
Let the zeroes of the quadratic polynomial be \( \alpha \) and \( \beta \).
From the given information:
\( \alpha + \beta = -5 \) and
\( \alpha \beta = 6 \)
Now, we need to find a quadratic polynomial with zeroes \( \alpha \) and \( \beta \).
The quadratic polynomial can be represented as:
\( (x - \alpha)(x - \beta) = 0 \)
Expanding this equation, we get:
\( x^2 - (\alpha + \beta)x + \alpha \beta = 0 \)
Substitute the values of \( \alpha + \beta \) and \( \alpha \beta \) into the equation:
\( x^2 - (-5)x + 6 = 0 \)
\( x^2 + 5x + 6 = 0 \)
Therefore, the quadratic polynomial with the sum of zeroes as -5 and the product of zeroes as 6 is \( x^2 + 5x + 6 = 0 \).