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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

    © BrainMass Inc. brainmass.com December 24, 2021, 8:16 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/methods-solving-quadratic-equations-262420

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    SOLUTION This solution is FREE courtesy of BrainMass!

    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, either 2x - 3 = 0 or x + 2 = 0
    On solving 2x + 3 = 0
    x = 3/2
    On solving x +2 =0
    x = - 2
    Therefore, the roots of the equation are {3/2, -2}.
    2. Solution of a Quadratic Equation by the method of Extraction of Roots:

    Quadratic Equation: 3x² - 125 = 0
    Solution:
    3x² = 75 (Isolate variable)
    X² = 25 (Divide by 3)
    x = ± 5 (Extract roots.)
    Therefore, the roots of the equation are {+5, -5}.
    3. Solving Quadratic Equations by Quadratic Formula

    The roots of the quadratic ax² + bx + c = 0 are given by [-b ± √(b2-4ac)]/2a

    Quadratic Equation: 3x² + 4x = 2
    Solution:
    3x² + 4x - 2 = 0 (Write in standard form.)
    a = 3, b = 4, c = -2

    The required roots of the equation are (-2+√10)/3 and (-2-√10)/3.
    c) The method of solving a Quadratic Equation by using Quadratic Formula is the easiest method and also, it can be applied to all forms of Quadratic Equations. So this method is the most preferred one above all the other methods

    Given: 3x2 - 5 = 16
    Solution: 3x2 = 16+5=21
    or x2 = 21/3 =7
    or, x = ±7
    Given: x2 + 10x = -9
    Solution: x2 +10x +9 =0
    or, x2 +10x +9+16 -16 =0
    or, x2 +10x +25 -16=0
    or, x2 + 2x5x +52 = 42
    or, (x + 5)2 = 42
    or, x +5 =±4
    or, x= -9, -1 which are the required roots.

    Given x2 - 7x +12 = 0
    Solving by Quadratic Formula,
    x = [7 ±√(49 -4*12)]/2 = [7±√1]/2 =[7+1]/2, [7-1]/2 = 4, 3
    Hence the required roots are 4 and 3.

    Solving by factorizing,
    x2 -7x +12 =0
    or, x2-4x -3x +12 =0
    or, x(x-4) -3(x-4)=0
    or, (x-4)(x-3) =0
    or, x =4, 3.

    Solving by completing the square,
    x2 -7x +12 =0
    or, x2 -7x +(7/2)2 +12 - (7/2)2 =0
    or, (x - 7/2)2 -1/4 =0
    or,( x-7/2)2= ¼
    or, x-7/2 = ±1/2
    or, x = 7/2+1/2, 7/2-1/2
    or, x = 4, 3.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 8:16 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/methods-solving-quadratic-equations-262420

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