The general form of a quadratic polynomial is given by:

$P(x) = x^2 - (S)x + P$

Where:

• $S$ is the sum of the zeroes.
• $P$ is the product of the zeroes.

Given that the sum of the zeroes is $5$ and the product of the zeroes is $-1$, we can substitute these values into the general form:

$P(x) = x^2 - (5)x + (-1)$

Thus, the quadratic polynomial is:

$P(x) = x^2 - 5x - 1$

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you derive the formula for the sum and product of the roots of a quadratic equation?
2. How do you factorize a quadratic expression like $x^2 - 5x - 1$?
3. Can the quadratic formula be used to find the roots of $x^2 - 5x - 1$?
4. How do you complete the square to solve $x^2 - 5x - 1 = 0$?
5. How do the sum and product of the roots relate to the coefficients of a quadratic equation?

Tip: The quadratic formula can always be used to find the roots of any quadratic equation, even if it cannot be easily factorized.