Find the complex zeros of the following polynomial function. Write f in factored form. x^4+2x^3+22x^2+50x-75 The complex zeros of f are ?

glamrockqueen7 2021-09-07 Answered
Find the complex zeros of the following polynomial function. Write f in factored form.
x4+2x3+22x2+50x75
The complex zeros of f are ?
Use the complex zeros to factor f.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

okomgcae
Answered 2021-09-08 Author has 93 answers

Step 1
Given function is,
f(x)=x4+2x3+22x2+50x75
The objective is to find the complex zeros of the function also write the function in factored form.
Step 2
Consider the function,
f(x)=x4+2x3+22x2+50x75
Since, x=1 satisfies the function.
Hence, (x1) is a factor of the function.
Then,
f(x)=x4+2x3+22x2+50x75
=x3(x1)+3x2(x1)+25x(x1)+75(x1)
=(x1)(x3+3x2+25x+75)
Now, x=3 also satisfy the function.
Hence, the (x+3) is a factor of the function.
Then function can be written as,
f(x)=(x1)(x3+3x2+25x+75)
=(x1)(x2(x+3)+25(x+3))
=(x1)(x+3)(x2+25)
Now, x=5iand5i satisfy the function.
Hence , function can be written as,
f(x)=(x1)(x+3)(x5i)(x+5i)
Therefore, the complex zeros of the function are x=5iand5i
Step 3
The function in factored form: f(x)=(x1)(x+3)(x5i)(x+5i)

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-09-08
Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
P(x)=12x2+2136x41000
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?
asked 2021-02-05
Use polar coordinates to find the limit. [Hint: Let x=rcosandy=rsin , and note that (x, y) (0, 0) implies r 0.] lim(x,y)(0,0)x2y2x2+y2
asked 2021-11-20
In a regression analysis, the variable that is being predicted is the
a. Intervening variable
b. Dependent variable
c. None
d. Independent variable
asked 2021-11-15
The electrical currents flowing in the antennas, during an MR imaging scan are given by:
3i3+3i15i2=7.5
i27i3+2i1=17.5
10i1+4i2+5i3=16
1. Write the above system of equations in the form Ax=b, where A is a 3 by 3 matrix and x and b are 3 by 1 vectors.
2. Find the determinant of A.
3. Determine i1, i2 and i3 by using Gaussian elimination.
asked 2021-11-16
In a certain city, the temperature (in F) at t hours after 9 AM is modeled by the function T(t)=50+14sin(πt12). Find the average temperature during the period from 9 AM to 9 PM.
asked 2021-02-27
Write formulas for the indicated partial derivatives for the multivariable function.
g(k,m)=k3m68km
a)gk
b)gm
c)gmk=2
asked 2021-10-02
Engineering statistics, i need solutions in 15 minutes please. MCQ/Engineering company has a task of checking compressive strength for 100 concrete cubes. The results revealed that 85 cubes passed the compressive strength test successfully and 15 cubes failed in the test. If 10 cubes are selected at random to be inspected by the company, determine the probability that the 8 cubes will pass the test and 2 cubes will fail in the test by using the Combinatorial Analysis. A-0.6553 B-0.2919 C-0.3415 D-0.4522 E-0.1156