# Methods of Solving Quadtratic Equations

1. There are four different methods to solve quadratic equations.

(a) List all 4 methods.

(b) Explain and give an example of 3 of those methods.

(c) Explain which method is preferred and why.

2. Solve the following problems.

a) Solve by using the even-root property.

3x - 5 = 16

b) Solve by using the following methods: factoring, completing the square, and the quadratic formula.

x + 10x = -9

c) Solve using the following methods: factoring, completing the square, and the quadratic formula.

x - 7x +12 = 0

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#### Solution Preview

a) The methods used to solve Quadratic Equations of the form ax2+bx+c = 0, are as follows:

1. Factorization

2. Extraction of Roots

3. Completing the Square

4. Quadratic Formula

b) Three methods of solving Quadratic equations with examples are as follows:

1. Solution of a Quadratic Equation by the method of Factorization:

Quadratic Equation: 10xÂ² + 5x = 30

Solution:

Write in standard from. 10xÂ² +5x -30 = 0.

On Factorizing L.H.S, 5(2xÂ² + x - 6) = 0

Again on Factorizing, 5(2x - 3)(x + 2) = 0

First factor is 5, which cannot be zero.

Therefore, ...

#### Solution Summary

This solution provides detailed explanations and step-by-step calculations of all methods involved in solving Quadratic Equations, along with examples. Each of the examples is solved by all the methods in order to provide a clear comparison between the various methods.