This document discusses solving quadratic equations by different methods such as factorisation, using the quadratic formula, and completing the square. It explains how to determine the number of solutions a quadratic equation has based on the sign of its discriminant, namely: - If the discriminant is positive, there are two real roots - If the discriminant is zero, there is one repeated root - If the discriminant is negative, there are no real roots. Examples are provided to illustrate calculating the discriminant and determining the number and type of roots.

1. Quadratic Equations
By the end of the lessson you will be able to :
• Solve quadratic equations by different methods.
• Anticipate the number of solutions of a
quadratic equation by studying its discriminant.

2. Quadratic equations
by factorisation
using GDC
by formula
by completing the square

3. Solve the equation:

4. Solve the equation:

5. Use the quadratic formula to solve the equation:

6. Simplify and then use your GDC to solve the
equation:

7. Use your GDC to solve the equations:

8. The quantity is called the
discriminant of the quadratic equation.
Δ > 0 ⇒
Δ = 0 ⇒
Δ < 0 ⇒
the equation has two real roots.
the equation has two equal roots.
the equation has no real roots.
qformula.wma

9. Δ > 0 Δ = 0
Δ < 0
Two different real roots
One repeated root
(or two equal roots)
No root.

10. Calculate the discriminant of the quadratic
expression
Hence show that is always positive

11. Find the possible values of the constant k such
that the equation
has one solution.

12. Consider the equation 2x2
+ kx +2 = 0 where k is a
constant. State for which values of k the equation
has
(a) two equal roots.
(b) no root.
(c) two distinct roots.

13. Solve Ex 1 D page 19

14. Attachments
qformula.wma