#Finding COmplex Roots

129 messages · Page 1 of 1 (latest)

weak spire
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I've got no idea how to find the complex roots of cubic equations
Help me find the complex roots for
(x-2)(x^2 +4x +5 + (46/x-2))

modest turtleBOT
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lime mantle
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like ax^2+bx+c but the discriminant is less than 0

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however, this one is not factorable in fact this is your answer which is not hand computable

E7C294E8-B13A-45FC-9942-DE49304D2B6E.png
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so are you meant to use a graphing calculator or something?

weak spire
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@lime mantle Help me solve one of these

image.png
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Maybe we'll do uhh

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lemme think

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number 13

lime mantle
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okay if this is no calculator i assume it is factorable

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so whatever you put there idk where you got that

fading solar
weak spire
lime mantle
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anyways, do you know the rational/integral root thereom

fading solar
weak spire
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yeah

weak spire
fading solar
weak spire
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its from a textbook

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I lied

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ok but

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Even with my calculator it wont give me complex roots

lime mantle
fading solar
lime mantle
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wait what are you putting into your calculator

weak spire
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x^3 - 2x^2 - 3x + 6

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And I have a ti-84 plus ce graphing calcukaltor

lime mantle
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okay so again

lime mantle
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basically what your cubics with complex roots will look something like

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(x^2+5)(x-3) or something

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or more complcated, (2x^2+3x+6)(x+4)

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but notice how we cannot factor down that quadratic

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it has no real solutions

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meaning it must have complex ones

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also, all polynomials with a degree of n must have n roots
if there are m real roots, then n-m of them are complex

weak spire
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Ok so

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how do I find the roots

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If I cant factor down the quadratic anymore

lime mantle
weak spire
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I dont think so

lime mantle
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like, find the complex roots of x^2+1

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huh ok

weak spire
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x^2 + 1 = 0

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x^2 = -1

lime mantle
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tldr just use quadratic formula

weak spire
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+- sqrt-1

weak spire
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i forgot

lime mantle
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yea

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surprised they didnt tell you that 💀

weak spire
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What do I do if theres an irregular remainder like

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45/x-2

lime mantle
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if there is a remainder

weak spire
lime mantle
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you did not successfully factor

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and you should try dividing by a different thing

lime mantle
weak spire
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thats dividing the polynomial

lime mantle
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mhm

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however

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when you factor you want to make the thing simpler

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the 4/(x-2) makes it more complicated

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so when youre trying to factor things above degree 3

weak spire
lime mantle
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do you know the remainder theorem

weak spire
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this equation has complex roots

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and i check my work everythings correct

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But idk how to fin dthe complex roots

lime mantle
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the problem is

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you dont know how to factor a cubic

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at least from what i see

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lets do that first

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and then the complex part comes after

weak spire
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I know how to

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divide polynomials

lime mantle
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yes however

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you need to know what to divide

weak spire
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like x^3 - 2x^2 + 5x +6/x+6

weak spire
weak spire
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in this server

lime mantle
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okay, so factor q13 then

weak spire
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think it was micabo

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"cubics cant b e factoroed

lime mantle
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actually

weak spire
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or they cant be factored conventially

lime mantle
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a vast majority of them cannot be factored

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however, if the question says no calculator you basically assume specific numbers are chosen such that it is factorable

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anyways

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hows factoring 13 going

weak spire
lime mantle
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what do you have so far

weak spire
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(x^4 - x^2)(-4)(x^3 -3x+3)

lime mantle
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and what work did you do to get that

weak spire
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rearanged terms and factored out -4 from

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-4x^3 + 12x -12

jagged sail
lime mantle
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you cant just vanish the x^4 lol

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what did you do exactly

weak spire
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idk man ill revist this tomorrow i gotta sleep

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thx

lime mantle
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alr gn

raw scroll
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just learn how to identify and use rational root theorem before you even start factoring quartics

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i believe your problem is that someone teaches/tells a method, you jump right into it and only stick with that method

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you need a toolbelt, not a singular tool

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and master all of the tools in your toolbelt before you start using them

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because then you could harm yourself and your learning

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so, learn to identify when to use certain tactics first before solving

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an no, i’m not being a “jerk”, i’m telling you the truth.

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you need to learn the concept for anything new you start learning before you start using it

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just please heed my advice

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if you don’t i can guarantee you’re going to be just as confused with anything you learn as you are now

fading solar
# raw scroll you need a *toolbelt*, not a singular tool

I think even that's a mistake. Viewing math as a series of discrete tools to be applied to seemingly arbitrary circumstances is itself damaging to learning. It's best to learn to see math as a unified system of logic and learn the proofs of why using a certain technique yields a particular result.

raw scroll
fading solar
raw scroll
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which was my OG point

sage sonnetBOT
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@weak spire

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runic lintel
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+close