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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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3 years ago

A soccer player uses her head to hit a ball up in the air from a height of 2 meters with an initial vertical velocity of 5 meter

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Answer:

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Step-by-step explanation:

The ball will hit the ground when its height is equal to 0 meters, therefore using this value in the expression and solving for "t" will give us the correct solutions.

$h = -4.9*t^2 + 5*t + 2\\\\-4.9*t^2 + 5*t + 2 = 0\\\\t_{1,2} = \frac{-5 \pm \sqrt{5^2 - 4*(-4.9)*(2)}}{2*(-4.9)}\\\\t_{1,2} = \frac{-5 \pm \sqrt{64.2}}{-9.8}\\\\t_{1,2} =\frac{-5 \pm 8.0125}{-9.8}\\\\t_1 = \frac{-5 - 8.0125}{-9.8} = 1.33 \text{ s}\\\\t_2 = \frac{-5 + 8.0125}{-9.8} = -0.3 \text{ s}$

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