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3 years ago

Write a polynomial equation with roots 5 and -9i. X^3-?x^2+?X-?=0

Mathematics

1 answer:

jek_recluse [69]3 years ago

6 0

Answer:

x³ - 5x² + 81x - 405 = 0

Step-by-step explanation:

Complex roots occur in conjugate pairs.

Thus given x = - 9i is a root then x = 9i is also a root

The factors are then (x - 5), (x - 9i) and (x + 9i)

The polynomial is the the product of the roots, that is

f(x) = (x - 5)(x - 9i)(x + 9i) ← expand the complex factors

= (x - 5)(x² - 81i²) → note i² = - 1

= (x - 5)(x² + 81) ← distribute

= x³ + 81x - 5x² - 405, thus

x³ - 5x² + 81x - 405 = 0 ← is the polynomial equation

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Read 2 more answers

If a spring is oscillating (moving) according to the velocity equation v(t) = 2sin(t) (in ft/s), then what is its displacement o

Feliz [49]

ANSWER

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EXPLANATION

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Answer:

step1 - distributive property

step2 - associative property

step3 - cumulative property

step4 - associative property

Step-by-step explanation:

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