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swat32
3 years ago
5

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

tandard form.
5, -3, and -1 + 3i
Mathematics
1 answer:
sergey [27]3 years ago
8 0

Answer:

y = x⁴ − 9x² − 50x − 150

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if -1 + 3i is a root, then -1 − 3i is also a root.

y = (x − 5) (x + 3) (x − (-1 + 3i)) (x − (-1 − 3i))

y = (x − 5) (x + 3) (x + 1 − 3i) (x + 1 + 3i)

Distribute using FOIL (first, outer, inner, last) to get real coefficients:

y = (x − 5) (x + 3) (x² + (1 + 3i)x + (1 − 3i)x + (1 − 3i)(1 + 3i))

y = (x − 5) (x + 3) (x² + x + 3ix + x − 3ix + 1 + 3i − 3i − 9i²)

y = (x − 5) (x + 3) (x² + 2x + 1 + 9)

y = (x − 5) (x + 3) (x² + 2x + 10)

Distribute to convert from factored form to standard form:

y = (x² + 3x − 5x − 15) (x² + 2x + 10)

y = (x² − 2x − 15) (x² + 2x + 10)

y = x²(x² + 2x + 10) − 2x(x² + 2x + 10) − 15(x² + 2x + 10)

y = x⁴ + 2x³ + 10x² − 2x³ − 4x² − 20x − 15x² − 30x − 150

y = x⁴ − 9x² − 50x − 150

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3 years ago
motorcycle cover 210 kilometre distance with 5 l of petrol how many kilometre does it cover with 8 litre of petrol? how much pet
Likurg_2 [28]

Answer:

A: 336 km

B: 14 L

Step-by-step explanation:

Use a proportion

210 km / 5 L = x / 8L         Cross multiply

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x = 1680 / 5

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===============

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Mrrafil [7]
\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------

\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\
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8 0
3 years ago
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adell [148]

Answer:

\boxed{\bold{\huge{\boxed{x = 26}}}}

Step-by-step explanation:

70 = \frac{4x+36}{2}

<u>Multiplying both sides by 2</u>

70 * 2 = 4x+36

140 = 4x+36

<u>Subtracting 36 to both sides</u>

140 - 36 = 4x

104 = 4x

<u>Dividing both sides by 4</u>

26 = x

OR

x = 26

3 0
3 years ago
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