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3 years ago

Write a polynomial equation of degree 4 in standard form that has the solutions i, −i, 1, −1.

Mathematics

1 answer:

Brut [27]3 years ago

4 0

Answer:

x⁴ + 2 x² + 1

Step-by-step explanation:

given solution of the polynomial

i, −i, 1, −1.

equation of the polynomial will be equal to

=(x - i)(x + i)(x - 1)(x + 1)

= (x² + i x - i x - i²)(x² + x - x + 1)

=(x² - (-1))(x² + 1 )

= (x² + 1)(x² + 1)

= x⁴ + x² + x² + 1

= x⁴ + 2 x² + 1

hence, the required polynomial equation is x⁴ + 2 x² + 1

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$t= \frac{-bplus minus \sqrt{ b^{2}-4ac } }{2a}$
You might recall seeing this as "x=..." but since our equation is in terms of t we use "t-=..."

In order to use the formula we need to identify a, b and c.
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Substituting these into the quadratic formula gives us:
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As we have "plus minus" (this is usually written in symbols with a plus sign over a minus sign) we split the equation in two and obtain:
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So the height is 8 feet at t = 3.63 and t=.12

It should make sense that there are two times. The ball goes up, reaches it's highest height and then comes back down. As such the height will be 8 at some point on the way up and also at some point on the way down.

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