Write a polynomial of minimal degree with integer coefficients that has the following information. Only have integer numbers in your answer. Zero Values: x = -3, 3+ 4i y-intercept: (0,-600)

Moises Woods

Moises Woods

Answered question

2022-09-04

Write a polynomial of minimal degree with integer coefficients that has the following information. Only have integer numbers in your answer.
Zero values: x = 3 ,   3 + 4 i
y-intercept: (0, -600)

Answer & Explanation

Adolfo Lee

Adolfo Lee

Beginner2022-09-05Added 17 answers

given that the zero values (roots) of a polynomial = -3, 3+4i
roots of conjugary of 3+4i=3-i4
let the polynomial of minimal degree
p ( x ) = y = a ( x x 1 ) ( x x 2 ) ( x x 3 ) y = a ( x + 3 ) ( x 3 4 i ) ( x 3 + 4 i ) y = a ( x + 3 ) ( ( x 3 ) 2 + 16 )
also given that y-intercept (0,-600)
So
600 = a ( 0 + 31 ( ( 6 3 ) 2 + 16 ) ) 600 = a ( 3 ) × 25 a = 600 3 × 25 = 8
So
y = 8 ( x + 3 ) ( ( x 3 ) 2 + 16 ) y = 8 ( x + 3 ) ( x 2 6 x + 9 + 16 ) y = 8 ( x 3 6 x 2 + 9 x + 16 x + 3 x 2 18 x + 27 + 48 ) y = 8 x 3 + 24 x 2 600
So polynomial y = 8 x 3 + 24 x 2 600 y = 8 x 3 + 24 x 2 + 56 x 600 y = 8 x 3 + 24 x 2 56 x 600

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