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

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swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0lol didnt know u were on

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

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1By reduce do you mean factor?

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

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1So 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.

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0Let me just see if I can follow what u did

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Take 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).

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0idk 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

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

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0OKKKK so like will this method always work?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Not 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.

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

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1You'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.

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0Haha So I hope and pray that it will be so. lol Thanks KGGGG
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