Cubic Equation | Find all roots
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- Äas pĆidĂĄn 14. 05. 2024
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Polynomials with order 3 have at most 3 solutions.
Arranging the eqn in another order:
x^3 - 27 = 0
x^3 - 3^3 = 0
(x - 3) (x^2 + 3x +9) = 0
Apparently, x = 3 and there are 2 more complex solutions which can be obtained by quadratic formula.
DONEđ
Perfect math channel, but please put the dividing line (supra, over) next to the equal sign, that's how it's done :)
just 3 seconds đ
Use Euler's formula for questions like this. (x/3)^3 = 1 = e^(2Ïi)=> roots e^0, e^(2Ïi/3), e^(4Ï/3).
Solutions 3 x the above list so 3, 3(-1 +â3 i)/2, 3(-1 - â3i)/2.
X=3
All solutions are 3, 3*e^(2/3pi* i) and 3 *(e^( 4/3pi* i)
In my simple mind, the answeres would be 3, and absolute value of 3 and -3, the remainder of the solutions seem to be changing the equation. Someone who is smarter than I am, please explain why you would care about creating a negative... this seems overly complicated for the sake of complicating it.
Only one cube root is 3...
Help (x+y)^x^1/2=(x-y)^y^1/2
2 Ń 2 = Đ„.
Đ„ = ?
Simply don't waste your time & viewer's time by writing many steps unnecessarily.
Read the question. How many roots. The answer is 3. And you want to waste our time. Go attend English classes
X=3