Formula For Constructing A Quadratic Equation
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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