Chapter 2 Quadratic Equations

1. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constant and a is not equal to 0.

2. The roots of a quadratic equation are the values of the unknown that satisfy the equation.

3. A quadratic equation ax^2 + bx + c = 0 can be solved by :
a) factorisation
b) completing the square
c) (-b ((+/-) (b^2 - 4 a c) ^(1/2))) / 2a

4. If a and b are roots of a quadratic equation, then the quadratic equation is (x - a) (x - b) = 0,
that is x^2 - (a + b)x + ab = 0.

In general, a quadratic equation is of the form:

x^2 - (sum of roots)x + (product of roots) = 0

5. Types of roots of a quadratic equation ax^2 + bx + c = 0 :
a) If b^2 - 4ac > 0, the equation has two different real roots.
b) If b^2 - 4ac = 0, the equation has two equal real roots.
c) If b^2 - 4ac < 0, the equation has no real roots.