How To Construct A Quadratic Equation Based On The Roots Of Other Quadratic Equations
Example:
Develop a quadratic equation whose roots are twice the roots of the quadratic equation x2 - 2x -10 = 0!
Answer:
Suppose that the equations of x2 - 2x - 10 = 0 are x1 and x2.
From the equation obtained:
a = 1
b = -2
c = -10
so:
x1 + x2 = -b/a
x1 + x2 = -(-2)/(1)
x1 + x2 = 2
x1 . x2 = c/a
x1 . x2 = -10/1
x1 . x2 = -10
Suppose that the roots of the new quadratic equation to be searched are α and β whose roots are twice the known root of the equation or α = 2x1 and β = 2x2.
α + β = 2x1 + 2x2
α + β = 2(x1 + x2)
α + β = 2(2)
α + β = 4
α . β = 2x1 . 2x2
α . β = 4x1 . x2
α . β = 4(-10)
α . β = -40
Then the new quadratic equation which has the roots of α and β is:
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Referensi :
- To'Ali's book math group accounting and sales
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