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    Methods of Solving Quadtratic Equations

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    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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    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: 10x² + 5x = 30
    Solution:
    Write in standard from. 10x² +5x -30 = 0.
    On Factorizing L.H.S, 5(2x² + 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.

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