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/sci/ - Science & Math

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5188464 No.5188464 [Reply] [Original]

So, I've got the polynomial

f(x) = 3x³ + 2x² - 19x + 16

How to get the roots ?
I know about polynomial divison, but how to get the first ?

>> No.5188470

Cubic formula

>> No.5188482

>>5188464
>horoscope
>>>/x/

>> No.5188491

approximate with newton's method

>> No.5188494

Check for rational roots first. You know that if a polynomial has integer coefficients then you can limit the rational roots to a small set of numbers.

>> No.5188492

>>5188464
Seriously op use any search engine of your choice, or just put it in wolframalpha. Stop shitting up the board with your homework

>> No.5188528

Cardano and then long division.

Tip: only 1 real root.

>> No.5188959

>>5188491
Agreed. Applied ftw

>> No.5188963

>>5188464
turners tablet you cunt. I love you, enjoy life.

>> No.5188976

>>5188464
>turners tablet
ah sry, seems like you dont call it that internationally....

It's this tablet you use to find out the roots of polynomial on any stage, 3rd and more

>> No.5189014

>>5188464
Just replace x by (plus or minus) 1, 2, 3, 4, 5, 6... until the equation adds up to zero, once this number if found, reverse it's sign (plus to minus, vise versa). You're root will be (x+/Your #/ or (x-/Your Number/ )

>> No.5189025

>>5189014
does that work if the root is not a whole number?

>> No.5189040

>>5188976
what exactly are you referring to?

>> No.5189049

>>5189014
the most brute force algorithm evar.

>> No.5189055

>>5189025
those are just the integers, so no. you will have to use decimals for rational numbers.
it definitely won't work for imaginaies

>> No.5189094

>>5189040

Where I live, we take in the equation ax^3+bx^2+cx+d=0(or higher), than use the rule that says that a number that is a factor of a or d, than try those factors devided by each other as possible roots, and use a table to see if they are real roots.

I don't know how to explain properly in engrish.

>> No.5189124
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5189124

>>5188464
Use Cardano's formulas.

>> No.5189177

>>5189094
We just refer to that as the rational root theorem.

>> No.5189193

>>5189177
ah thanks alot, yes looks like that was what i was meaning:)

The tablet we than use to determine if it's an actual root is a danish invention, don't know if it's widespread too

>> No.5189269
File: 42 KB, 253x320, 1350951453276.png [View same] [iqdb] [saucenao] [google]
5189269

>>5188464
<span class="math">\frac{Factors~of~the~last~number}{Factors~of~the~first~number} [/spoiler]

There may not be a rational (or real) solutions though...

>> No.5189298

rational roots test first. Than use the rule of signs/bound limits if that fails.

Or be lazy like me and have your Ti-nspire do it for you.