2. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.
For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

3. Roots is just another word for solutions !
e.g. Find the roots of the equation
Completing the square:
Solution: There are no factors, so we can either complete the square or use the quadratic formula.
Using the formula:
(1)
(2)

4. The answers from the quadratic formula can be simplified:
We have
However,
4 is a perfect square so can be square-rooted, so
So,
2 is a common factor of the numerator, so
Numbers such as are called surds
We have simplified the surd

5. The part is called the discriminant
The roots are real and equal.
The roots are not real.
The roots are real and distinct.
( different )
The Discriminant
The formula for solving the quadratic equation is
If we try to solve an equation with no real roots, we will be faced with the square root of a negative number!

6. The roots are real and distinct.
( different )
The discriminant
e.g. For

7. The discriminant
e.g. For
The roots are real and equal.

8. There are no real roots as the function is never equal to zero.
The discriminant
e.g. For