We have several methods we can use to solve **quadratic equations**. To determine which method is the most suitable we need to look at the form of the quadratic equation.

There is not one correct method for solving a quadratic equation. You would not be wrong by using one method over another; it is just easier, sometimes more practical, to use some methods over others.

For the following quadratic equations, find the solution using an efficient method. Justify which method you used.

a

x^2-7x+12=0

Worked Solution

b

x^2-11=21

Worked Solution

c

3x^2-24x+20=5

Worked Solution

A rectangular enclosure is to be constructed from 100 meters of wooden fencing. The area of the enclosure is given by A = 50 x - x^{2}, where x is the length of one side of the rectangle. If the area is 525 \text{ m}^2, determine the side lengths.

Worked Solution

Idea summary

Below is a list of the easiest method to use and the form of the quadratic equation for which we should use it:

Easiest equation form: | |
---|---|

Graphing | \text{Any form is fine when using technology} |

Factoring | ax^2+bx+c=0\text{ where }a,b,c\text{ are small} |

Square root property | x^2=k\text{ or }a(x-h)^2=k |

Completing the square | x^2+bx+c=0\text{ where }b\text{ is even} |

Quadratic formula | ax^2+bx+c=0\text{ where }a,b,c\text{ are large } |