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anonymous
 one year ago
(x(5+8i))(x+(5+8i))
anonymous
 one year ago
(x(5+8i))(x+(5+8i))

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rishavraj
 one year ago
Best ResponseYou've already chosen the best response.0(a  b)(a + b) = a^2  b^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that doesnt help me though because i already knew that but this equation is far more difficult and i's are involved @rishavraj

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, but we usually put the "real" component first (tradition) 39+80i

phi
 one year ago
Best ResponseYou've already chosen the best response.1that is the b^2 in a^2  b^2 a^2 is x^2 so the answer is x^2 ( 39+80i) or x^2 +39 80 i

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay thank you so much

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i also have to multiply it by (x4) and (x+14) or (x^2+10x56) how would i do that? @phi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because when i do it i get terms with both an i and an x and i dont know how to simplify that

phi
 one year ago
Best ResponseYou've already chosen the best response.1painfully. you want to do (x^2 + (39 80 i)) (x^2+10x56) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah haha i tried and it just gets too confusing after awhile

phi
 one year ago
Best ResponseYou've already chosen the best response.1if we write it this way ,so we have "real" and imaginary terms: \[( (x^2+39)  80i) (x^2+10x56) \] and distribute the (x^2+10x56) we get \[ (x^2+39) (x^2+10x56) + 80(x^2+10x56) i \] the first part gives a 4th order polynomial the second part (with the "i") will be the imaginary part. (we leave the "i" on the outside)

phi
 one year ago
Best ResponseYou've already chosen the best response.1no matter how you write it, it will be an ugly expression.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i didnt know you could do that. so should i distribute it all out?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont even know how to distribute the imaginary part

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for the first part i got \[x ^{4}+10x ^{3}17x ^{2}+390x2184\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1for the imaginary part, you could distribute the 80 to get (80x^2800x+4480) i but multiplying it out really depends on what you plan to do next. Personally I would leave things factored... unless there is a reason to multiply things out.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i would leave it factored also but the question was this: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, 14, and 5 + 8i

phi
 one year ago
Best ResponseYou've already chosen the best response.1oh. In that case we want *** real coefficients **** and that means its roots come in complex conjugates in other words (oh my!) we should start 5+8i and 58i (notice the 8i)

phi
 one year ago
Best ResponseYou've already chosen the best response.1thus we would do (x  (5+8i))(x  (5 8i))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wow i just realized that okay thank you

phi
 one year ago
Best ResponseYou've already chosen the best response.1or, collecting the real part \[ ( (x5) 8i) ( (x5) + 8i) \] the answer is a^2  b^2 where a is (x5) and b is 8i

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so should i foil x5 first?

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, FOIL (x5)(x5) you get \[ (x5)^2  (64 i^2) \\ x^2 10x +25 + 64 \] notice the very convenient fact, the imaginary part disappears

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes thank god then what about the other roots 4 and 14? do i just multiply (x4) and (x+14) into that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay thank youuuuuu ill tell you what i get

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ ( x^2 10x +89)(x4)(x+14) \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay i got \[x ^{4}67x ^{2}+1450x4984\] sorry it took so long @phi

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[x^467 x^2+1450 x4984\] looks good
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