Solution to Quadratic Equations

A quadratic equation is an equation that can be written in the form:

where:

� = coefficient of �

� = coefficient of �

� = constant

Example:

Therefore:

Method 1: Factorization

Consider:

We need two numbers that:

multiply to give +6

add to give -5

They are -2 and -3.

Therefore:

So:

Therefore:

Hence:

Teaching Point

Factorization is usually quick when the quadratic factors easily.

Method 2: Completing the Square

Consider:

Move the constant:

Take half of the coefficient of �:

Square it:

Add 9 to both sides:

Therefore:

Take the square root:

Therefore:

So:

Important Reminder

When taking the square root, students must remember the ± sign.

Method 3: Quadratic Formula

For:

the quadratic formula is:

Example

Solve:

Here:

Substitute:

Therefore:

or

Hence:

The Discriminant

Introduce:

The discriminant helps determine the nature of the roots.

Discriminant

Nature of roots

�

Two distinct real roots

�

Two equal real roots

�

No real roots