$MathMaster logo$

MathMaster

Home
general
suppose i tell you that one root of a polynomial function f x is 4 3i what must also be a root of f x

Question

Suppose I tell you that one root of a polynomial function, f(x), is 4+3i . What must also be a root of f(x)?

281

likes

1404 views

Answer to a math question Suppose I tell you that one root of a polynomial function, f(x), is 4+3i . What must also be a root of f(x)?

$Expert avatar$

4.6

110 Answers

1. Given that \(4+3i\) is a root.
2. For polynomials with real coefficients, complex roots always appear in conjugate pairs.
3. Therefore, the complex conjugate \(4-3i\) must also be a root.

Answer:

4-3i

Frequently asked questions (FAQs)

What is the area of a rectangle with length 10 units and width 7 units?

+

Find the period of the function f(x) = 2cos(3x) + sin(2x) - tan(5x) + 4sec(x) - cot(4x)

+

What is the derivative of f(x) = x^2 - 3x + 1 with respect to x?

+

New questions in Mathematics

A=m/2-t isolate t

a to the power of 2 minus 16 over a plus 4, what is the result?

Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1

The function g:Q→Q is a ring homomorphism such that g(3)=3 and g(5)=5. What are the values of g(8) and g(9)?

how many arrangements can be made of 4 letters chosen from the letters of the world ABSOLUTE in which the S and U appear together

Let f(x) = x² − 1. Find the equation of the tangent line to the graph of f at the point x0 = 2.

There were no defectives in a sample of 1 light bulb does this sample provide sufficient evidence that in the warehouse with millions of light bulbs fewer than 10% are defective?

6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.

The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. b) What is the profit value made by the hotel for one

The maximum gauge pressure of a hydraulic ramp is 16 atm, with a support area whose diameter is 20 cm. What is the mass of the heaviest vehicle that can be lifted?

Buffalo Company makes and sells shampoo. Each unit requires $1.40 labor costs, material costs per unit are $0.90 and other variable costs are $0.30. It sells shampoo for $4.45 to retailers. Fixed costs are $15,000. It sold 25,000 units in the current month. What is the Break-Even point in units? What is the Break-Even point in dollars? What is the contribution margin of Buffalo Company?

A loan is repaid with payments of $2226 made at the end of each month for 12 years. If interest on the loan is 5.2%, compounded semi-annually, what is the initial value of the loan? Enter to the nearest cent (two decimals). Do not use $ signs or commas.

In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1

1. The cost to transport 250 packages of cement 120 kilometers is $600. What will be the cost to transport 500 packages 300 kilometers?

Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?

12[4 + (8 + 7) + 5]

I have a complex function I would like to integrate over. I can use two approaches and they should give the same solution. If I want to find the contour integral ∫𝛾𝑧¯𝑑𝑧 for where 𝛾 is the circle |𝑧−𝑖|=3 oriented counterclockwise I get the following: ∫2𝜋0𝑖+3𝑒𝑖𝑡⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯𝑑(𝑖+3𝑒𝑖𝑡)=∫2𝜋03𝑖(−𝑖+3𝑒−𝑖𝑡)𝑒𝑖𝑡𝑑𝑡=18𝜋𝑖 If I directly apply the Residue Theorem, I would get ∫𝛾𝑧¯𝑑𝑧=2𝜋𝑖Res(𝑓,𝑧=0)=2𝜋𝑖