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
MArishka [77]
2 years ago
14

Suppose $p(x)$ is a monic cubic polynomial with real coefficients such that $p(3-2i)=0$ and $p(0)=-52$. determine $p(x)$ (in exp

anded form).
Mathematics
1 answer:
Maslowich2 years ago
3 0

If p(3-2i)=0, then complex number 3-2i is a root of cubic polynomial.

If polynomial has real coefficients, then conjugated 3+2i is also a root of polynomial.

Then the polynomial will be of a form

p(x)=(x-(3-2i))(x-(3+2i))(x-a).

Since p(0)=-52, then

-52=(0-(3-2i))(0-(3+2i))(0-a),\\ \\-52=(2i-3)(3+2i)a,\\ \\-52=(4i^2-9)a,\\ \\-52=(-4-9)a,\\ \\-13a=-52,\\ \\a=4.

Therefore,

p(x)=(x-(3-2i))(x-(3+2i))(x-4),\\ \\p(x)=(x^2-6x+13)(x-4),\\ \\p(x)=x^3-10x^2+37x-52.

You might be interested in
Find the modulus of -2 - 6i.<br><br> 40<br> -40<br> 6.3<br> -6.3
olga2289 [7]
The modulus of complex number can be computed with this equation:
|z|=sqrt(Re(z)^2+Im(z)^2)
z = -2-6i
Re(z)=-2, so Re(z)^2=4
Im(z)=-6, so Im(z)^2=36
|z|=sqrt(36+4)=sqrt(40)=6.3
6 0
2 years ago
Jim has for cups of milk he wants to find the number of 1/4 cup serving in his four cups of milk draw a model to find how many 1
IgorC [24]
16 is the answer :)))
5 0
2 years ago
Adding 5 to a number and then doubling the result gives the same answer as multiplying the number by 5 and then adding 1. What i
chubhunter [2.5K]

32-54+4+ 7y=4

boom son

6 0
3 years ago
How many digits are there in Hindu- Arabic system
kobusy [5.1K]
10 digits.
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
5 0
2 years ago
Create your own unit rate example in which you have to determine the unit rate of two fractions with different units. Explain wh
levacccp [35]
I’m sorry but i don’t know what it is
7 0
2 years ago
Other questions:
  • What are the common factors between 100 50 an 30
    6·1 answer
  • 3 please it would really help (4 would give u brainliest)
    12·1 answer
  • How can the tiles be sorted? (I need it quick please)
    9·1 answer
  • What is (3-4i)^2? In complex numbers?
    5·1 answer
  • What is the measure of AC?
    15·1 answer
  • Find the dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm2. (Let x, y, and z be
    9·1 answer
  • Please find the area of the trapezoids.<br> By the way, the answer is NOT 10.5.
    13·1 answer
  • Evaluate the following expressions: plz help me <br> 0.65 x 10^2<br> 1.1 X 10^3<br> 0.56 x 10^3
    9·1 answer
  • You are a volunteer at a physical therapy clinic. A set of stairs you use to help patients is shown with its dimensions. What is
    10·1 answer
  • SOMEONE PLEASE HELP ME...
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!