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3 years ago

What is the least possible degree of a polynomial that has roots -5,1 + 4i, and -4i?

Mathematics

1 answer:

Oksanka [162]3 years ago

6 0

Without any extra conditions, the answer could be 3, and the simplest polynomial with the given roots would be

(<em>x</em> + 5) (<em>x</em> - (1 + 4<em>i</em> )) (<em>x</em> + 4<em>i</em> )

= <em>x</em> ³ + 4<em>x</em> ² + (11 - 4<em>i</em> ) <em>x</em> + 80 - 2<em>i</em>

<em />

If the polynomial is supposed to have only <em>real</em> coefficients, then any complex roots must occur along with their complex conjugates:

(<em>x</em> + 5) (<em>x</em> - (1 + 4<em>i</em> )) (<em>x</em> - (1 - 4<em>i</em> )) (<em>x</em> + 4<em>i</em> ) (<em>x</em> - 4<em>i </em>)

= <em>x</em> ⁵ + 3<em>x</em> ⁴ + 23<em>x</em> ³ + 133<em>x</em> ² + 112<em>x</em> + 1360

and then the degree would be 5.

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TiliK225 [7]

Answer: 1/9

Step-by-step explanation:

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3 years ago

Given the conversion factor 12 in/ 1 ft, which has the larger volume?

dsp73

Answer:

A. Cube A

Given:

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2 years ago

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I'm so confused, pls help

Vera_Pavlovna [14]

Answer:

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Step-by-step explanation:

(18x + 36) / 3 = 6x + 12

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-6x . -6x

12 = -16 + 2x

+16 . +16

28 = 2x

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3 years ago

Find the amount after 2 years for 25000 at 10% pa compounded annually and halfyearly

Molodets [167]

Answer:

8358.7

Step-by-step explanation:

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2 years ago

Total blood cholesterol level was measured for each of

laiz [17]

<h3>Answer: Mean = 218.9.</h3><h3>Median = 229</h3><h3>Mode = Zero mode.</h3>

Step-by-step explanation:

Given blood cholesterol level was measured for each of 8 adults (in mg/dL) are:

264, 191, 160, 148, 262, 212, 268, 246

In order to find the mean, we need to add all those 8 numbers and divide by 8.

Therefore, mean = $\frac{264+191+160+148+262+212+268+246}{8} =\frac{1751}{8} =218.9.$

In order to find the median, we need to arrange them in ascending order:

148, 160, 191, 212, 246, 262, 264, 268.

The middle most two values are 212 and 246.

Therefore, median = $\frac{212+246}{2} =\frac{458}{2} = 229.$

<h3>Median = 229.</h3>

$\mathrm{The\:mode\:is\:the\:term\:in\:the\:data\:set\:that\:appears\:the\:most.}$

$\mathrm{If\:there\:is\:more\:than\:one\:term\:that\:appears\:the\:most,\:then\:there\:is\:no\:mode.}$

$\mathrm{Count\:the\:number\:of\:times\:each\:element\:appears\:in\:the\:list}$

$\begin{pmatrix}148&160&191&212&246&262&264&268\\ 1&1&1&1&1&1&1&1\end{pmatrix}$

$\mathrm{The\:most\:common\:element\:is\:not\:unique,\:so\:there\:is\:no\:mode}$

<h3>Therefore, Mode = Zero mode.</h3>

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3 years ago