Math Contest #23 [2 SBI]

in #puzzle2 years ago

Here you can keep your brain fit by solving math related problems and also earn SBI or sometimes other rewards by doing so.
The problems usually contain a mathematical equation that in my opinion is fun to solve or has an interesting solution.
I will also only choose problems that can be solved without additional tools(at least not if you can calculate basic stuff in your head), so don't grab your calculator, you won't need it.


No upvote, No resteem, No follow required!

I will give the SBI(s) randomly to any participants.

You have 4 days to solve it.



Find all zeros(including complex ones!) of the following polynomial:
P(x) = x⁴ + 8x³ + 24x² + 32x + 15

P(x) = 0
Solve for x!


To everyone who already participated in a past contest, come back today and try a new problem(tell me if you don't want to be tagged):
@addax @ajayyy @athunderstruck @bwar @contrabourdon @crokkon @fullcoverbetting @golddeck @heraclio @hokkaido @iampolite @kaeserotor @masoom @mmunited @mobi72 @mytechtrail @ninahaskin @onecent @rxhector @sidekickmatt @sparkesy43 @syalla @tonimontana @vote-transfer @zuerich

In case no one gets a result(which I doubt), I will give away the prize to anyone who comments.


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You can support him by using a witness vote on untersatz, so he can further support this and other contests.


Took a similar approach as zuerich. with the try-out solutions (-1 &-3) and polynom division, the complex part can be reduced:

P(x) = x^4 + 8x^3 + 24x^2+ 32x + 15
     = (x + 3)(x^3 + 5x^2 + 9x + 5)
     = (x + 3)(x + 1)(x^2 + 4x + 5)
     = (x + 3)(x + 1)(x + 2 + i)(x + 2 - i)

Solving each bracket for 0 gives all zeros of the polynom => Solutions: -3, -1, -2-i, -2+i

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via trying: -1 and -3;
rest: x^2+4x+5

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