Quadratic Equations

Quadratic Equations

Introduction
In Senior Two, you dealt with expansions which led to quadratic expressions / equations, and you solved them using their factors. In this topic, you will explore more about quadratic equations, by solving them using various methods. Quadratic equations can help you to understand situations that happen in real life, such as the rise and fall of profits from selling goods / services, the decrease or increase in the
amount of time it takes a person to cover a kilometre — based on ones age, and so on.
An interesting part of having something that can be modelled by a quadratic equation is that you can easily solve the equation and even predict future patterns. In this topic, you will understand and solve quadratic equations and relate them to
graphs.
12.0 Reviewing Quadratic Expressions / Equations
You learnt about quadratic expressions, their expansions, and factorisations in Senior
Two. You also looked at solving quadratic equations using factorisation.
Activity 12.0 (Work in groups)

Determining the roots of quadratic equations using factorisation This method uses the concept of factors as discussed in Senior Two.
Activity 12.1 (b) (Work in groups)
Draw any rectangle whose length is morethan the width by 2.
(a). Label the dimensions of the rectangle clearly.
(b)Form an algebraic expression in relation to area of the rectangle.
(c) Form a quadratic equation if the area of the rectangle is 130 squared units.
(d) Use the dimensions and area to write down a quadratic equation.
A school has a rectangular garden with an area of 1800 m2. Its length is 30 m
longer than the width. Find the dimensions of the garden.

12.5 Solving Simultaneous Equations Involving one Quadratic Equation and a Linear Equation
In Topic 70, you learnt how to solve simultaneous equations involving two linear equations using substitution, elimination and graphs. You will use the same ideas to solve simultaneous equations involving one quadratic equation and a linear
equation.
Using substitution method to solve simultaneous equations involving one quadratic equation and a linear equation