Cubic polynomial with leading coefficient of 1 and zeros 4 and 5i

Question

Mathematics

Jonathan Lewis

2 January, 21:30

Cubic polynomial with leading coefficient of 1 and zeros 4 and 5i

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Answers (1)

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Alvaro · Answer 1

Where there is a zero, a+bi, there is a zero, a-bi

therfor since there is a zero 0+5i, there is also a zero 0-5i

zeroes are 4, 5i,-5i

for zeroes

r1, r2, r3

the factors are

(x-r1) (x-r2) (x-r3)

so

(x-4) (x-5i) (x+5i)

expand

f (x) = x^3-4x^2+25x-100