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
(x^4 + 2x^2 + 1) - (4x^2 + 400x + 10000) = 0
(x^2 + 1)^2 - (2x + 100)^2 = 0
(x^2 + 2x + 101) * (x^2 - 2x - 99) = 0
x^2 + 2x + 101 = 0 OR x^2 - 2x - 99 = 0
x^2+2x+1 = -100 OR x^2-2x+1 = 100
(x+1)^2 = (10i)^2 OR (x-1)^2 = 10^2
x+1 = +/-10i OR x-1 = +/-10
x = -1+/-10i OR x = 1+/-10
x = -1-10i OR x = -1+10i OR x = -9 OR x=11
Edited to correct sign error and subsequent incorrect answer.
Edited on October 13, 2024, 10:41 pm
Solution
