From 18670260285d25b14921a89fae60089da334c921 Mon Sep 17 00:00:00 2001 From: altaf-creator Date: Mon, 25 Sep 2023 20:18:57 +0700 Subject: Unlocked website, added rationalising roots --- .../quadratic-equation/finding-suitable.html | 117 +++++++++ lessons/matematika/quadratic-equation/index.html | 277 +++++++++++++++++++++ 2 files changed, 394 insertions(+) create mode 100644 lessons/matematika/quadratic-equation/finding-suitable.html create mode 100644 lessons/matematika/quadratic-equation/index.html (limited to 'lessons/matematika/quadratic-equation') diff --git a/lessons/matematika/quadratic-equation/finding-suitable.html b/lessons/matematika/quadratic-equation/finding-suitable.html new file mode 100644 index 0000000..9e13f01 --- /dev/null +++ b/lessons/matematika/quadratic-equation/finding-suitable.html @@ -0,0 +1,117 @@ + + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + + + + +
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+ Firstly, lets use this equation.
+
+

Step-by-step

+
    +
  1. Find the factors of c, which in this equation, c = 30.
    2. +
  2. The factors of 30 are: +
      +
    • 1, 30
      • +
    • 2, 15
      • +
    • 3, 10
      • +
    • 5, 6
      • +
    +
    3. +
  3. Lets define that the first and second factors are y1, 2. To find the suitable factors for the equation, you need to check if; +
      +
    • , and
      • +
      • +
    +
    4. +
  4. Check for each of the factors. We end up with 5 and 6.
    5. +
  5. So, the answer is 5 & 6
    6. +
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Introduction

+ In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x + represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.[1] +

Formula / Format

+ ax2 + bx + c = 0 +

+ a, b, c = known numbers, where a ≠ 0
+ x = the unknown, or the root +

+

Exercises

+

Finding the roots with factorisation.

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    +
  1. + +

    +

    + To find the answer, we need to find the factors of c that is suitable for b and c. What and how do I find the suitable factors?
    + The suitable factor for the equation are 2 and -3.
    + Then, insert each numbers to this formula: , where y is the factor.

    +

    +
    + So, the answer is +

    + +
    2. +
  2. +

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    + Factors: 2, 4
    +

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    + +
    3. +
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Relation between Quadratic Equation and Algebraic Expressions

+

This is an algebraic expression → . You can turn that into a quadratic equation.

+ + +

Quadratic Equation's Root Operations

+

Finding Quadratic Equation with Roots

+

You can use the formula below to find a Quadratic Equation with 2 roots.

+ , where x1, 2 are the roots.
+

+ Example:

+ +

+ +

Quadratic Root's Mathematical Operations

+

Formulas

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Examples

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  1. +

    Diketahui persamaan kuadrat , memiliki akar-akar persamaan kuadrat x1 dan x2. Jika x1 < x2, maka tentukan: +

      +
    1. x1 + x2
      2. +
    2. x1 × x2
      3. +
    +

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      2. +
      3. +
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References

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  1. Quadratic Equation - The English Wikipedia, https://en.wikipedia.org/wiki/Quadratic_equation
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