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melomori [17]
3 years ago
7

Find a third-degree polynomial equation with rational coefficients that has roots -4 and 6 + i.

Mathematics
1 answer:
dolphi86 [110]3 years ago
3 0

Answer:

x³ - 8x² - 11x + 148

Step-by-step explanation:

Given that x = 6 + i is a root then x = 6 - i is also a root

Complex roots occur as conjugate pairs.

The factors are therefore (x - (6 + i)) and(x - (6 - i))

Given x = - 4 is a root then (x + 4) is a factor

The polynomial is the product of the factors, that is

p(x) = (x + 4)(x - (6 + i))(x - (6 - i))

      = (x + 4)(x - 6 - i)(x - 6 + i)

      = (x + 4)((x - 6)² - i²)

      = (x + 4)(x² - 12x + 36 + 1)

      = (x + 4)(x² - 12x + 37) ← distribute

      = x³ + 4x² - 12x² - 48x + 37x + 148

      = x³ - 8x² - 11x + 148

 

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swat32
If they each kept the same amount of the $50 prize, then we divide $50 by 2 people, giving each of them $25 winnings.  Your question is then a little confusing because it could be answered in two ways.  Did they each keep $20.75 out of their $25 winnings, or did the two of them keep $20.75 in a combined total?  Please read your question again to see which might be the case.  I'm answering on the assumption that they each kept $20.75.


STEP 1:
divide total prize money by 2

= $50 ÷ 2
= $25 each won


STEP 2:
If they each kept $20.75

= $25 won - $20.75 each kept
= $4.25 each gave away


STEP 3:
multiply amount given away by 2 people
= $4.25 * 2 people
= $8.50 total given away


ANSWER: The total given to Romy is $8.50.

Hope this helps!  :)
8 0
3 years ago
How many whole sandwiches can be made with 3 pounds of turkey if each sandwich has 5 ounces of turkey on it? 4 6 9 10
Svetradugi [14.3K]
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6 0
3 years ago
Read 2 more answers
F(x) = 2x + 5
Finger [1]

9514 1404 393

Answer:

  15. f(x) +g(x) = 7x +2

  16. f(x) -g(x) = -3x +8

  17. h(x) · g(x) = 35x -21

Step-by-step explanation:

Substitute the function definition for each function expression and simplify.

__

15. f(x) + g(x) = (2x +5) +(5x -3)

  f(x) +g(x) = 7x +2

__

16. f(x) - g(x) = (2x +5) -(5x -3)

  f(x) -g(x) = -3x +8

__

17. h(x) · g(x) = (7) · (5x -3)

  h(x) · g(x) = 35x -21

4 0
3 years ago
obtain the equation of two points passing of lines 4x-3y-1=0 and 2x-3y+3=0 and equally inclined to the axes​
klasskru [66]

Answer:By 8(4)P.5, the slope of the line equally inclined to axes is tan(±45  

o

)=±1. Hence by P+λQ=0,

5λ+3

2λ+4

​

=±1

⇒λ=  

3

1

​

,−1. Putting for λ, the two lines are

x−y=0,x+y−2=0.

Was this answer helpful

8 0
2 years ago
-p/3 - 8 = -3 I need the show work too
professor190 [17]

Answer:

-15

Step-by-step explanation:

-3+8-5. 5x3=15 and because it is -p it would be -15.

3 0
2 years ago
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