HSC Together Year 11 Maths Extension: Roots of a Quadratic Polynomial

#### Maths Extension

• Further Work with Functions
• Polynomials
• Inverse Trigonometric Functions
• Further Trigonometric Identities
• Rates of Change
• Working with Combinatorics
• Back to other subjects
Back to other subjects

# Roots of a Quadratic Polynomial

There’s a couple of ways to work out the roots of a polynomial, and one of the easier ways to do this is using the coefficients! This is part of the Prelim Maths Extension 1 Syllabus from the topic Functions: Polynomials. In this post, we will explore Sums and products of roots of polynomials roots of a quadratic polynomial. Here we will learn to solve problems using the relationships between the roots and coefficients of quadratic, cubic and quartic equations.

Relevant equations for this topic include the following:

ax^2 + bx + c   -(\alpha + \beta + \gamma) x^2+ (\alpha \beta +\alpha \gamma + \gamma \beta)x - \alpha \beta \gamma

Where the three roots are:

• \alpha
• \beta
• \gamma

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