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Reduce the polynomial and find its complex roots
\(f(x)=x^4+5x^39x^285x136\)
 one year ago
 one year ago
Reduce the polynomial and find its complex roots \(f(x)=x^4+5x^39x^285x136\)
 one year ago
 one year ago

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swissgirlBest ResponseYou've already chosen the best response.0
lol didnt know u were on
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
not quite sure how to reduce it since u start dealing with decimals. It shld be quite simple though
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
By reduce do you mean factor?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Well, I have a couple ideas, so let's see if I can do this by hand... \[f(x)=x^4+5x^39x^285x136\\ f(x)=x^417x^2+5x^3+8x^217(5x8)\\ f(x)=x^417x^2+x^2(5x+8)17(5x+8)\\ f(x)=x^417x^2+(x^217)(5x+8)\\ f(x)=x^2(x^217)+(x^217)(5x+8)\\ f(x)=(x^217)(x^2+5x+8) \]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
So you can use the quadratic formula on \(x^2+5x+8\) to find the complex roots, and just \[x^217=0\implies x=\pm\sqrt{17}\]For the real roots.
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
Let me just see if I can follow what u did
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Take your time. I'm honestly very surprised I was able to factor that almost entirely by hand. (I used wolfram to check correctness, and to find the gcd of 85, 136).
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
idk if its possible. Dont drive urself crazy buttt I cant decipher what is squred and what is tripled. Is it possible to make it larger
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
\[\Large f(x)=x^4+5x^39x^285x136\\ \Large f(x)=x^417x^2+5x^3+8x^217(5x8)\\ \Large f(x)=x^417x^2+x^2(5x+8)17(5x+8)\\ \Large f(x)=x^417x^2+(x^217)(5x+8)\\ \Large f(x)=x^2(x^217)+(x^217)(5x+8)\\ \Large f(x)=(x^217)(x^2+5x+8)\]
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
OKKKK so like will this method always work?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Not always. This is just factoring by grouping, and while potentially useful, it is often difficult to identify the correct time to use it, and what to group together. I just got lucky that I guessed the right things to group. For example, if I had \[\Large f(x)=x^4+5x^310x^285x136\]instead, I would not be able to group it as easily.
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
ohhhh i seee. I guesss I have to play around. Not as simple as I wish it wld be. Thanks KG:)))))))))))
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
You're welcome. I will note however, that if they tell you to factor something, it's usually possible to do it by hand with a little cleverness.
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
Haha So I hope and pray that it will be so. lol Thanks KGGGG
 one year ago
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