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    Ax BX +C 0 Ax BX +C 0: Grade 9 Summarized Module

    Uploaded by

    Israel Marquez
    The document summarizes solving quadratic equations. It defines a quadratic equation as an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Examples are provided of quadratic and non-quadratic equations. Methods for solving quadratic equations include extracting square roots, factoring, completing the square, and using the quadratic formula. Specific steps and examples are outlined for solving by square root and factoring.

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    Ax BX +C 0 Ax BX +C 0: Grade 9 Summarized Module

    Uploaded by

    Israel Marquez
    43 views2 pages
    The document summarizes solving quadratic equations. It defines a quadratic equation as an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Examples are provided of quadratic and non-quadratic equations. Methods for solving quadratic equations include extracting square roots, factoring, completing the square, and using the quadratic formula. Specific steps and examples are outlined for solving by square root and factoring.

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    GRADE 9 SUMMARIZED MODULE

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    The document summarizes solving quadratic equations. It defines a quadratic equation as an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Examples are provided of quadratic and non-quadratic equations. Methods for solving quadratic equations include extracting square roots, factoring, completing the square, and using the quadratic formula. Specific steps and examples are outlined for solving by square root and factoring.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    43 views2 pages

    Ax BX +C 0 Ax BX +C 0: Grade 9 Summarized Module

    Uploaded by

    Israel Marquez
    The document summarizes solving quadratic equations. It defines a quadratic equation as an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Examples are provided of quadratic and non-quadratic equations. Methods for solving quadratic equations include extracting square roots, factoring, completing the square, and using the quadratic formula. Specific steps and examples are outlined for solving by square root and factoring.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 2

    GRADE 9

    SUMMARIZED MODULE

    QUADRATIC EQUATION

    III-MOST ESSENTIAL LEARNING COMPETENCIES

    The learner illustrates quadratic equations. Solves quadratic equations by extracting the square
    roots, factoring, completing the square and using the quadratic formula.

    An equation that can be written in the form ax 2 +bx +c=0 , where a, b and c are real numbers
    with a≠ 0, is a quadratic equation in general form. The name quadratic comes from “quad” meaning
    square. If the quadratic equation is written ax 2 +bx +c=0 in which all the nonzero terms on the left side
    equating to 0, it is said to be a quadratic equation in general form. A quadratic equation is called a second
    degree equation because the left side is a polynomial of degree 2.

    Here are more examples:

    2 x2 +5 x +3=0 It is a quadratic equation in which a=2, b=5 and c


    =3
    x 2+ 3 x =0 You don’t usually write “1 x2” thus a=1, b=3 and 3
    is not shown, because c=0
    5 x+ 3=0 The term of degree 2 is missing, which means a=0.
    By definition this equation can never be called
    quadratic. It is a linear equation.

    Illustrative examples

    Write each of these quadratic equation in general form and identify the real numbers a, b and c.

    1. m 2 +7 m−8=0

    Solution

    m 2 +7 m−8=0 it is already in general form, where a=1, b=7 and c= -8

    2. 4 x2 −3 x =5

    Solution
    4 x2 −3 x −5=0 the equation in general form. Thus a=4, b=-3 and c=-5

    SOLVING QUADRATIC EQUATIONS BY THE SQUARE ROOT

    Example:

    Solve for x: x 2=16

    Solution:

    Get all the terms on the same side by addition x 2−16=0


    property of equality (difference of two squares)
    By the addition property of equality 2
    x =16
    Extract the square root x=4,x= -4
    List all the value of x. x={4,-4}

    SOLVING QUADRATIC EQUATIONS BY FACTORING

    Example:

    Solve for x: x 2−x=6

    Solution:

    Here are the steps you should follow:

    1. Move all terms to the same side of the equal sign, so x 2−x−6=0
    the equation is set equal to 0. This places the equation in general form
    2. Factor the algebraic expression (x-3)(x+2) are called factors. These are
    the factors of the equation x 2−x−6 .
    3. Set each factor equal to 0.this process is called the x-3=0; x+2=0
    “zero product property”. If the product of two factors
    equal to 0, then either one or both of the factors must
    be 0.
    4. Solve each resulting equation. x=3 and x= -2 are called roots. These are
    the roots of the equation x 2−x−6=0

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