The polynomial in question is: x^4−8x^3−19x^2+288x−612 and the zero is 4−i.

aphathalo 2022-10-08 Answered
The polynomial in question is:
x 4 8 x 3 19 x 2 + 288 x 612
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Answers (1)

Farbwolkenw
Answered 2022-10-09 Author has 6 answers
Taking a polynomial for factorization such as
x 4 8 x 3 19 x 2 + 288 x 612
and with a given root 4−i, it is clear that the polynomial has only real coefficients, and therefore there is a second root 4+i. So we take these roots together like so:
( x 4 i ) ( x 4 + i ) = ( x 4 ) 2 i 2 = x 2 8 x + 17
Then we have a quadratic that we can use as a divisor on the original:
x 2 8 x + 17 x 4 8 x 3 19 x 2 + 288 x 612
I get
( x 2 8 x + 17 ) ( x 2 36 ) = x 4 8 x 3 19 x 2 + 288 x 612
which means that the remaining factors are (x−6),(x+6) .
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