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Triss [41]
2 years ago
7

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and 3−

i.
Mathematics
1 answer:
Neko [114]2 years ago
5 0

Answer:

P(x) = x^3 - 10x^2+ 34x-40

Step-by-step explanation:

Given

p =1 -- Leading coefficient

Zeros: 4\ and\ 3  - i

Required

Determine the polynomial

Represent the zeros with a and b

Such that

a = 4

b = 3 - i

The polynomial is:

P(x) = p * (x - a) * (x - b)

P(x) = 1 * (x - 4) * (x - (3 - i))

However, to solve further: We need to symmetrise over 3-i  and its conjugate

P(x) = 1 * (x - 4) * (x - (3 - i))* (x - (3 + i))

P(x) =  (x - 4) * (x - (3 - i))* (x - (3 + i))\\\\

To define a suitable function, the expression becomes

P(x) =  (x - 4) * ((x - 3)^2+1)

P(x) =  (x - 4) * ((x - 3)(x - 3)+1)

P(x) =  (x - 4) * (x^2 - 6x + 9+1)

P(x) =  (x - 4) * (x^2 - 6x +10)

Open bracket

P(x) = x^3 - 6x^2 +10x - 4x^2 + 24x-40

P(x) = x^3 - 6x^2  - 4x^2+10x + 24x-40

P(x) = x^3 - 10x^2+ 34x-40

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Two sides of a triangle
True [87]

step 1: open brackets n rmb to flip the signs

step 2 (optional): rearrange to make the equation clearer to add/minus

length of 3rd side:

(8x + 3) - (2x + 1) -(5x + 2)

= 8x + 3 - 2x -1 - 5x -2

= 8x -2x -5x +3 -1 -2

= x

Therefore, length of 3rd side is X cm.

---

If perimeter = 75cm,

8x +3 = 75

8x = 75-3

8x = 72

x = 9 cm

Therefore,

1st side = 2(9) +1

= 19 cm

2nd side = 5(9) +2

= 47 cm

3rd side = 9 cm

4 0
3 years ago
What is the slope, x intercept, y intercept for this question: 1/3x+ 1/2y= 9
Sergeeva-Olga [200]
Hope this helps you 3y=54-2
6 0
2 years ago
A well of diameter 4m is dug 14m deep. The earth taken out is spread evenly all around the well to form a 40cm high embankment.
dimulka [17.4K]

Answer:

82.72m

Step-by-step explanation:

Volume = πr2h

= 3.142*7*7*14

= 2,155.41m³

Now that we hav the volume of earth, we go on to find the raduis of the spread

2155.41m³ = 3.142*r²*0.4

2155.41m³ = 1.26r²

r² = 1,710.64

r = 41.36m

Width = diameter = 2r = 82.72m

8 0
3 years ago
A student committee is to consist of 2 freshmen, 5 sophomores, 4 juniors, and 3 seniors. If 6 freshmen, 13 sophomores, 8 juniors
mezya [45]
<h3>Answer:  491,891,400</h3>

Delete the commas if necessary.

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

Explanation:

There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.

Plug n = 6 and r = 2 into the nCr combination formula below

n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\

This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.

Repeat those steps for the other grade levels.

n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.

You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.

Similarly, 8C4 = 70 is the number of ways to pick the juniors.

Lastly, 14C3 = 364 is the number of ways to pick the seniors.

-----------------------------

To recap, we have...

  • 15 ways to pick the freshmen
  • 1287 ways to pick the sophomores
  • 70 ways to pick the juniors
  • 364 ways to pick the seniors

Multiply out those values to get to the final answer.

15*1287*70*364 = 491,891,400

This massive number is a little under 492 million.

7 0
2 years ago
Please help me :))) :PPPPPP
Korolek [52]

I prefer decimals with common denominators so I'm going to go ahead and convert them.

-1.25+.50 = -.75

-.75 is -3/4 aka "c" or the third option.

8 0
3 years ago
Read 2 more answers
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