Quadratic Functions

The Discriminant The expression b 2 − 4 a c in the general formula is called the discriminant of the equation, as it determines the type of roots that the equation has. Example Determine the nature of the roots of the following equations. a. 5 x 2 − 7 x + 3 = 0 b. … Read more

2.4.1 Finding the Sum of Roots (SoR) and Product of Roots (PoR) Example Find the sums and products of the roots of the following equations. a. x 2 + 7 x − 3 = 0 b. x ( x − 1 ) = 5 ( 1 − x ) Answer: (a) x 2 + 7 … Read more

2.4 Forming Quadratic Equations from Given Roots Let α and β be the roots of the equation ax2 + bx + c = 0, this means Example: Find the quadratic equation from the respective roots below: (a) 3, −1 (b) −2, ¼ (c) ⅔, ¼ (d) 3m, −2m Solution: Click on the image below to … Read more

The quadratic equation a x 2 + b x + c = 0 can be solved by using the quadratic formula − b ± b 2 − 4 a c 2 a Example  Use the quadratic formula to find the solutions of the following equations. a. x 2 + 5 x − 24 = 0 … Read more

2.3.2 Solving Quadratic Equations – Completing the Square(A) The Perfect Square 1. The expression x2 + 2x + 1 can be written in the form (x + 1)2, it is called a “perfect square”.   2. If the algebraic expression on the left hand side of the quadratic equation is a perfect, the roots can be easily obtained … Read more

2.3.1 Solving Quadratic Equations – Factorisation 1. If a quadratic equation can be factorised into a product of two factors such that (x – p)(x – q) = 0 Hence  x – p = 0   or  x – q = 0    x = p   or x = q p and q  are the roots of the equation. Notes … Read more

Solving Quadratic Equations To solve a quadratic equation means to find all the roots of the quadratic equations. Example: Find the roots of the quadratic equations a. x 2 = 9 b. 2 x 2 − 98 = 0 Answer:  (a) x 2 = 9 x = ± 9 x = ± 3 (b) 2 … Read more

Roots of Quadratic Equations Roots of a quadratic equation are the values of variables/unknowns that satisfy the equation. Example: Determine whether 1, 2, and 3 are the roots of the quadratic equation x 2 − 5 x + 6 = 0 . Answer: When x = 1, x 2 − 5 x + 6 = … Read more

General Form of Quadratic EquationGeneral form of a quadratic equation isax2 + bx + c = 0where a, b, and c are constants and a≠0.*Note that the highest power of an unknown of a quadratic equation is 2. Example (Find the values of a, b and c)Rewrite the following into the general form of a … Read more