Polynomials

The zeroes of a polynomial are the x-coordinates where its graph cuts or touches the x-axis. A linear polynomial has one zero, a quadratic can have at most two, and a cubic can have at most three real zeroes.

For quadratic polynomials ax² + bx + c, the sum of zeroes is -b/a and the product is c/a. Similar coefficient relations can be written for cubic polynomials as well, and these are extremely useful in verification and equation formation.

Although the contents page may not list it separately here, school work often connects this chapter to dividing one polynomial by another. It supports factorisation, remainder ideas and solving algebraic questions efficiently.

Students should finish the chapter knowing how graphs show zeroes, how to connect zeroes with coefficients, and how to use these relations in direct problems and proofs.