Formula For Constructing A Quadratic Equation

If x₁ and x₂ are roots of a quadratic equation, then the equation of the quadratic equation is:

1. Multiplication Factor Formula

Formula:

(x - x₁)(x - x₂) = 0

Example:
Find the quadratic equation with -2 and 5 as the roots!

Answer:
For example:
x₁ = -2
x₂ = 5

(x - x₁)(x - x₂) = 0
(x - (-2))(x - 5) = 0
(x + 2)(x - 5) = 0
x² - 5x + 2x - 10 = 0
x²  - 3x - 10 = 0

Thus the quadratic equation which has the respective roots -2 and 5 is x²  - 3x - 10 = 0.

2. Product Formulas of The Roots

x² - (x₁ + x₂)x + x₁ . x₂ = 0

Example:
Find the quadratic equation with -2 and 5 as the roots!

Answer:
x₁ = -2
x₂ = 5

x₁ + x₂ = -2 + 5 = 3
x₁ . x₂ = -2 . 5 = -10

x²  - (x₁ + x₂)x + x₁ . x₂ = 0
x² - (3)x + (-10) = 0
x² - 3x - 10 = 0

Thus the quadratic equation which has the respective roots -2 and 5 is x² - 3x - 10 = 0.

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Referensi :

• To'Ali's book math group accounting and sales

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