1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
poizon [28]
3 years ago
5

Find a polynomial P(x) with real coefficients having a degree 4, leading coefficient 4, and zeros 3-i and 4i.

Mathematics
1 answer:
Alisiya [41]3 years ago
3 0

now, this polynomial has roots of 3-i and 4i, namely 3 - i and 0 + 4i.

let's bear in mind that a complex root never comes all by her lonesome, her sibling is always with her, the conjugate, so if 3 - i is there, 3 + i is also coming along, likewise if 0 + 4i is there, her sibling 0 - 4i is also there.

\bf \begin{cases} x=3-i\implies &x-3+i=0\\ x=3+i\implies &x-3-i=0\\ x=4i\implies &x-4i=0\\ x=-4i\implies &x+4i=0 \end{cases}\\\\[-0.35em] ~\dotfill\\\\ (x-3+i)(x-3-i)(x-4i)(x+4i)=\stackrel{y}{0} \\[2em] \underset{\textit{difference of squares}}{[(x-3)+i][(x-3)-i]}\underset{\textit{difference of squares}}{[x-4i][x+4i]}=0

\bf [(x-3)^2-i^2][x^2-(4i)^2]=y\implies [(x-3)^2-(-1)][x^2-(4^2i^2)]=0 \\[2em] [(x-3)^2-(-1)][x^2-(16(-1))]=0\implies [(x-3)^2+1][x^2+16]=0 \\[2em] [(x^2-6x+9)+1][x^2+16]=y\implies (x^2-6x+10)(x^2+16)=0 \\\\\\ x^4-6x^3+10x^2+16x^2-96x+160=0 \\\\\\ x^4-6x^3+26x^2-96x+160=0 \\\\\\ \stackrel{\textit{multiplying both sides by 4}}{4(x^4-6x^3+26x^2-96x+160)=4(0)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 4x^4-24x^3+104x^2-384x+640=y~\hfill

You might be interested in
Disjoint, Independent, and Complement State whether the two events (A and B) described are disjoint, independent, and/or complem
just olya [345]

Answer:

Independent Events

Step-by-step explanation:

Two events are mutually exclusive or disjoint if they cannot both occur at the same time.

Two events are independent if the probability of occurrence of one does not affect the probability of occurrence of the other.

The complement of any event B is the event [not B], i.e. the event that B does not occur.

Australia plays Argentina for the championship in the Rugby World Cup.

At the same time, Ukraine plays Russia for the World Team Chess Championship.

A = event that Argentina wins their rugby match.

B = the event that Ukraine wins their chess match.

The two events A and B are Independent as the outcome of one does not affect the outcome of the other

4 0
3 years ago
During a food drive, a local middle school collected 8,887 canned food items. Each of the 27 classrooms that participated in the
leva [86]
8,887 cans divided by 27 classrooms is 329.1481 so each class donated about
329 cans
3 0
3 years ago
An item cost 50 is marked up 20% off.Sales tax for the item is 8%.What is the final price including tax?
sashaice [31]

$64.80 50+20%+8% tax then you get 64.80

4 0
3 years ago
What is five ninths plus four sixths
Minchanka [31]

Answer: 1.22222222222

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
PLEASE HELP ALSO WILL GET THE BRAINIEST ANSWER!!!! ALSO SHOW YOUR WORK!!!!
MAVERICK [17]
I=PRT
I=Interest
P=principal
R=rate in decimal
T=time in years

1year=12months
72months/12months=6 years
t=6

given
I=8925
P=35000
R=r
T=6


8925=35000*r*6
8925=210000*r
divide both sides by 210000
0.0425=r

the interest rate is 4.25%
6 0
3 years ago
Read 2 more answers
Other questions:
  • He coordinates below represent two linear equations.
    15·1 answer
  • 18-3n+2=n+20-4n which is the solution 0 (0) or all reals
    6·1 answer
  • Which answer is it? I just learned this today, so I'm confused.​
    9·1 answer
  • Please anybody help me out
    9·1 answer
  • A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. she estimates that for each addit
    15·1 answer
  • Water evaporates at a rate of 1.5 ounces per day from a container that holds 34 ounces when . What is an expression that represe
    13·1 answer
  • I need help with this asapp
    12·1 answer
  • Kevin works as a part-time vendor selling wallets for $20 each and hats for $15 each. He needs to earn a minimum of $450 per wee
    11·1 answer
  • Solve 8m-2(14-m)>7(m-4)+3m
    5·1 answer
  • Math!! please please helppp!!!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!