QUADRATIC EQUATIONS IT LESSON 1  NATURE OF
ROOTS
(SEC 3 ADDITIONAL MATHS)
Software: LiveMath
(previously known as MathView)
Thinking Skills: Induction
and Deduction
At the end of the lesson, the students should be able to:
(1) identify the three types of roots for a quadratic equation,
(2) explain how the discriminant determines the nature of these roots,
(3) explain how the nature of these roots affects the number of points
of intersection of the quadratic curve and the xaxis.
A. INVESTIGATION
If you cannot view the LiveMath
document below, click here to
troubleshoot.

B. INDUCTION
1.  Observe the values of the discriminants and the types of
roots of the equations. Infer by induction
how you will identify the type of roots for a quadratic equation without
finding their actual values.

2.  Explain why the discriminant affects the type of roots for a quadratic
equation.

3.  What relationship do you observe between the type of roots of a quadratic
equation and how the graph of the corresponding quadratic expression cuts
the xaxis?

C. EXERCISE
1.  Do NOT use your computer to do the exercise. 
2.  Calculate the discriminants of the following quadratic equations and hence deduce the types of roots they have. 
3.  Sketch the graphs of the corresponding quadratic expressions including the xaxis. 

Equation 
D=b²–4ac 




2 equal real roots? 2 nonreal roots? 







4–5x–x²=0 














–9+12x–4x²=0 

