Let us consider this quartic equation:
x4- 2x2 - 400x = 9999
Find all possible roots of the above equation.
x^4 - 2x^2 - 400x - 9999 = 0
From the rational root theorem ...
Factors of 9999 are ± {1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999}
Checking all 24 finds 2 roots: {-9, 11}
So (x+9) and (x-11) are factors.
x^4 + 9x^3 - 9x^3 - 81x^2 + 79x^2 + 711x - 1111x - 9999 = 0
(x+9)(x^3 - 9x^2 + 79x - 1111)
(x+9)(x-11)(x^3 - 11x^2 + 2x^2 - 22x + 101x - 1111)
(x+9)(x-11)(x^2 + 2x + 101)
Final 2 roots from quadratic equation: -1 ± √(1-101)
roots: {-9, 11, -1+10i, -1-10i}
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Posted by Larry
on 2024-10-13 21:50:45 |
solution
