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Yuri [45]
3 years ago
10

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

tandard form. (5 points) 4, -8, and 2 + 3i
f(x) = x4 - 6x3 + 12x2 - 90x + 416
f(x) = x4 - 45x2 + 180x - 416
f(x) = x4 - 35x2 + 180x - 416
f(x) = x4 - 6x3 - 12x2 + 90x - 416

Mathematics
1 answer:
Nataly_w [17]3 years ago
3 0
<h3>Answer: Choice C) x^4-35x^2+180x-416</h3>

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

Explanation:

The given zeros are: 4, -8, 2+3i

All coefficients are real numbers, so this means that the root 2+3i must be paired with 2-3i which is its conjugate pair.

While we are given 3 roots, there are actually four roots and they are: 4, -8, 2+3i, 2-3i

This means,

x = 4 or x = -8 or x = 2+3i or x=2-3i

x-4=0 or x+8=0 or x-2=3i or x-2=-3i

x-4=0 or x+8=0 or (x-2)^2=(3i)^2 or (x-2)^2=(-3i)^2

x-4=0 or x+8=0 or (x-2)^2=-9 or (x-2)^2=-9

x-4=0 or x+8=0 or (x-2)^2=-9

x-4=0 or x+8=0 or (x-2)^2+9=0

(x-4)(x+8)((x-2)^2+9)=0

(x-4)(x+8)(x^2-4x+4+9)=0

(x-4)(x+8)(x^2-4x+13)=0

(x^2+4x-32)(x^2-4x+13)=0

x^4-35x^2+180x-416 = 0 .... see attached image below

If you work your way backwards up the steps listed here, then you'll go from x^4-35x^2+180x-416 = 0 to x = 4 or x = -8 or x = 2+3i or x=2-3i

This shows f(x) = x^4-35x^2+180x-416 has the four roots x = 4, x = -8, x = 2+3i, x = 2-3i

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Suppose that fanf g are continuous functions,
shtirl [24]

The required result based on given continuous functions is: 207. See the explanation for same below.

<h3>What are continuous functions?</h3>


A continuous function in mathematics is one in which a continuous variation (that is, a change without a jump) of the argument causes a continuous variation of the function's value.

<h3>What is the calculation for the above solution?</h3>

Since G and F are continuous functions,

\int_{12}^{28}) \, f(x) dx = 19

\int_{12}^{28}) \, f(x) dx = 35

Therefore,

\int_{12}^{28}) \, [K g(x) - 2 f(x)] dx

= K \int_{12}^{28}) \, g(x) dx -2 \int_{12}^{28}) \, f(x) dx

So, given that K = 7, we have

7 x 35 - 2 x 19
= 245 - 38
= 207

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7 0
1 year ago
Sixty students took a math test. The percentages of students who scored an A, B, C, or D are displayed in the circle graph, but
GarryVolchara [31]

Answer:

30

Step-by-step explanation:

8 0
3 years ago
What is (30 1/9 + 4 1/3) - 19 5/6
weqwewe [10]
14 11/18
I got this answer by doing 30 1/9 + 4 1/3= 34 4/9
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3 years ago
Find the difference. (7x-6 2/3) - (-3x + 4 3/4)
NikAS [45]

10x-61/12 is the difference of  (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4}).

<h3>What is Expression?</h3>

An expression is combination of variables, numbers and operators.

The given expression is (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4})

7x-6\frac{2}{3}+3x- 4\frac{3}{4}

7x-20/3+3x-19/4

Add the variable terms and constant terms.

10x-20/3-19/4

The LCM of 3 and 4 is 12/

10x-4-57/12

10x-61/12

Hence, 10x-61/12 is the difference of  (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4}).

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4 0
1 year ago
Help please I do not know how to do this
sleet_krkn [62]

Answer:

0 and 1

Step-by-step explanation:

If a polynomial P(x) is divided by (x + h), then by the Remainder theorem

The remainder is the value of P(- h)

(1)

For P(x) divided by (x - 1) , then the remainder is P(1) = 0

(2)

For P(x) divided by (x + 2) then the remainder is P(- 2) = 1

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3 years ago
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