Formula For Constructing A Quadratic Equation

If x1 too x2 are roots of a quadratic equation, thence the equation of the quadratic equation is:

1. Multiplication Factor Formula

Formula:
(x - x1)(x - x2) = 0

Example:
Find the quadratic equation amongst -2 too 5 every bit 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 - x = 0
x2  - 3x - x = 0

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

2. Product Formulas of The Roots

x2 - (x1 + x2)x + x1 . x2 = 0

Example:
Find the quadratic equation amongst -2 too 5 every bit the roots!

Answer:
x1 = -2
x2 = 5

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

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

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

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Referensi :
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