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netineya [11]
3 years ago
7

A degree 4 polynomial P(x) with integer coefficients has zeros 5 i and 3, with 3 being a zero of multiplicity 2. Moreover, the c

oefficient of x^4 is 1. Find the polynomial.
Mathematics
1 answer:
Sergio039 [100]3 years ago
6 0

Multiplicity is how many times the root repeats

roots r1 and r2 of a polynomial factor to

(x-r1)(x-r2)

so 3 multiplicty 2 means (x-3)^2 is in the factorization of that polynomial


also, for a polynomial with real coefients, if a+bi is a roots, a-bi is also a root

5i is a root, therefor -5i is a root as well


roots are

(x-5i)(x+5i)(x-3)^2

if we expand

x^4-6x^3+34x^2-150x+225

the polynomial is

f(x)=x^4-6x^3+34x^2-150x+225


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First find the decimal equivalent of square root 3: SQRT(3) = 1.732 ( roughly)
 
If the base and height were each 3, then the hypotenuse would need to be:

3^2 + 3^2 = C^2
9 + 9 = C^2
18 = C^2
C = SQRT(18) = 4.24

This is larger than sqrt(3), so this cannot be a right triangle.


If one leg was 3 and the other leg was sqrt(3) then the hypotenuse would be:
3^2 + 1.73^2 = C^2
9 + 3 = C^2
12 = C^2
C = SQRT(12) = 3.46

This is larger than 3, this cannot be a right triangle.

The answer is b) no.





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Answer:

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Your part time job pays you $14/h. You work approximately 12 hours/week.
kirill115 [55]

Answer:

  1. <u>BOX 1 </u>=  672.00

(14 * 12 = 168

168 * 4 = $ 672 )

     2. <u>BOX 2</u> = 282.95

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12 .50 * 4   = 50   (4 WEEKS A MONTH )

Transportation =  131.2 A MONTH

32.80 * 4 = 131.2  (4 WEEKS A MONTH )

Movie =  $16.75 A MONTH

Charity = $ 40 A MONTH

10 * 4  (4 WEEKS A MONTH )

<u> MONTHLY EXPENSE </u> = 45 + 50 + 131.2 + 16.75 + 40

<u> MONTHLY EXPENSE </u> = 282.95 )

      3. <u>BOX 3</u> = 389.05

Money that can be saved = Monthly income - Monthly expense

Money that can be saved = 672 -  282.95

                                          = 389.05

<h2><em><u>please give brainliest </u></em></h2>
4 0
3 years ago
Which expression represents the distance between the points (11, 4) and (5,8)?
antiseptic1488 [7]

Answer:

\displaystyle d = 2\sqrt{13}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)

<u>Algebra II</u>

  • Distance Formula: \displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (11, 4) → x₁ = 11, y₁ = 4

Point (5, 8) → x₂ = 5, y₂ = 8

<u>Step 2: Find distance </u><em><u>d</u></em>

Simply plug in the 2 coordinates into the distance formula to find distance <em>d</em>

  1. Substitute in points [Distance Formula]:                                                       \displaystyle d = \sqrt{(5-11)^2+(8-4)^2}
  2. [√Radical] (Parenthesis) Subtract:                                                                 \displaystyle d = \sqrt{(-6)^2+(4)^2}
  3. [√Radical] Evaluate exponents:                                                                    \displaystyle d = \sqrt{36+16}
  4. [√Radical] Add:                                                                                               \displaystyle d = \sqrt{52}
  5. [√Radical] Simplify:                                                                                         \displaystyle d = 2\sqrt{13}
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Answer:

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Step-by-step explanation:

7 0
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