Find a polynomial P(x) with real coefficients having a degree 6, leading coefficient 5, and zeros 7, 0 (multiplicity 3) and 2 - 3i.

Roselyn Daniel

Roselyn Daniel

Answered question

2022-07-28

Find a polynomial P(x) with real coefficients having a degree 6, leading coefficient 5, and zeros 7, 0 (multiplicity 3) and 2 - 3i

Answer & Explanation

Ryan Hahn

Ryan Hahn

Beginner2022-07-29Added 11 answers

Solution:
P ( x ) = 5 ( x 7 ) ( x 0 ) 3 ( x ( 2 3 i ) ) ( x ( 2 + 3 i ) ) P ( x ) = 5 x 3 ( x 7 ) ( x 2 + 3 i ) ( x 2 3 i ) P ( x ) = ( 5 x 4 35 x 3 ) ( ( x 2 ) 2 ( 3 i ) 2 ) P ( x ) = ( 5 x 4 35 x 3 ) ( x 2 + 4 4 x 9 i 2 ) P ( x ) = ( 5 x 4 35 x 3 ) ( x 2 + 4 4 x + 9 ) P ( x ) = 5 x 6 55 x 5 + 205 x 4 455 x 3

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