The quadratic polynomial whose sum of zeroes is 5 and product of zeroes is -1 is

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.

Find the quadratic polynomial with a sum of zeroes equal to 5 and a product of zeroes equal to -1. This problem explores key algebraic concepts, including the general form of quadratic polynomials and Vieta's formulas, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation