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Liono4ka [1.6K]
3 years ago
15

Write a polynomial with rational coefficients having roots 3,3+i and 3-i

Mathematics
1 answer:
Elena L [17]3 years ago
3 0
Part 1: If the roots of a polynomial are a, b, and c, then the factors can be written in the form (x - a), (x - b), and (x - c). In this case, we have (x - 3), (x - [3 + i]), and (x - [3 - i]). The three factors are (x - 3)(x - 3 - i)(x - 3 + i).

Part 2: The two factors with complex terms are (x - 3 - i)(x - 3 + i), and multiplying these terms as a difference of two squares can give:
(x - 3)^2 - i^2 = x^2 - 6x + 9 - (-1) = x^2 - 6x + 10

Part 3: We now multiply (x^2 - 6x + 10) by the remaining factor of (x - 3). This results in the cubic expression:
(x^2 - 6x + 10)(x - 3)
= x^3 - 3x^2 - 6x^2 + 18x + 10x - 30
= x^3 - 9x^2 + 28x - 30
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Answer:

4104.79 Seconds or about 1.14 Hours

Step-by-step explanation:

26mi = 41842.9m

100/9.81 = 41842.9/x

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7 0
3 years ago
What is the solution of 3+ x-2/x-3 less than or equal to 0
bagirrra123 [75]

Answer:

The solution set consists of all the real numbers smaller than or equal to 11/4:

x\leq \frac{11}{4}

Step-by-step explanation:

We need to solve for x (that means isolate x on one side of the inequality symbol) in the following inequality:

3+\frac{x-2}{x-3} \leq 0\\\frac{x-2}{x-3} \leq -3\\x-2\leq -3\,(x-3)\\x-2\leq -3x+9\\x+3x\leq 9+2\\4x\leq 11\\x\leq \frac{11}{4}

4 0
3 years ago
Simplify the expression: (19^1/9)^9
andrey2020 [161]
(19^1/9)^9=

19^1/9•9=

1/9•9=1

your answer would be 19 hope dis helps :)
5 0
3 years ago
Ariel is working at meat -packing plant 5 night a weak .Her regular wage is $11 an hour.She earns time and a half for any overti
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Answer:

$148.50.

Step-by-step explanation:

Hourly wage for time and a half = 11 * 1.5

=$16.50

For 9 hours she earns 16.50 * 9

= $148.50.

4 0
3 years ago
A boat starts in Wilmington and sails 5 miles due east and then 3 miles due south. What is the approximate shortest distance bac
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Step-by-step explanation:

(This answer may be wrong)

7 0
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