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
Umnica [9.8K]
3 years ago
12

According to the Complex Conjugate Root Theorem, if a+bi is a root of a quadratic equation, then __blank__ is also a root of the

equation. Which expression correctly completes the previous sentence?
a−bi
a+bi
−a−bi
−a+bi
Mathematics
1 answer:
Trava [24]3 years ago
3 0

Answer:

a-bi


Step-by-step explanation:

If a quadratic equation lx^2+mx+n=0 has one imaginary root as a+bi then the other root is the conjugate of a+bi = a-bi

Because we have l, m and n are real numbers and they are the coefficients.

Sum of roots = a+bi + second root = -m/l

When -m/l is real because the ratio of two real numbers, left side also has to be real.

Since bi is one imaginary term already there other root should have -bi in it so that the sum becomes real.

i.e. other root will be of the form c-bi for some real c.

Now product of roots = (a+bi)(c-bi) = n/l

Since right side is real, left side also must be real.

i.e.imaginary part =0

bi(a-c) =0

Or a =c

i.e. other root c-bi = a-bi

Hence proved.


You might be interested in
Manny was given the equation (x+2)(x-7)=0 and asked to find the zeros. The solutions he came up with were x=2 and x=-17.
Inessa [10]

Answer:

see explanation

Step-by-step explanation:

Given

(x + 2)(x - 7) = 0 ← in standard form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 7 = 0 ⇒ x = 7

Thus the zeros are x = - 2 and x = 7

3 0
3 years ago
Help me all please!!
Harlamova29_29 [7]
No matter how many pizzas he orders (P) he will be charged 4.50. then each pizza is worth 9.50 so you multiply that by how many he orders (5)
c=4.5+9.5p 
c=4.5+9.5(5)
c=$52

for these problems you do the opposite of what is shown
1. h+7=15, subtract 7 from each side. h=8
2. m-10=24, add 10 to each side m=34
3.6t=96, divide both sides by 6 t=16
4. multiply both sides by 7, p=21. 

7 0
3 years ago
Read 2 more answers
How many hours must you run if you want to run 27 km at a rate of 9 km/h? (Apex)
Nuetrik [128]

Answer:

3

Step-by-step explanation:

27 km

9 km every hour

so 27/9=3

7 0
3 years ago
3.75 written as a word
tigry1 [53]
Three and seventy five hundredths............Hope I Helped! PS: I am a Middle Schooler and I know this! 
7 0
3 years ago
An<br>5. A train travelled 720 km in 9 h. How far<br>would it travel in 11 h?​
Citrus2011 [14]

Answer:

The train would travel 880 km in 11 hours.

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • What is a contra?? thanks :)
    10·2 answers
  • The area if the of a circle is 111.6 square centimeters. What is the diameter?
    13·2 answers
  • Find the value of x. <br> PLEASE HELP ME!!
    5·1 answer
  • Here is a variation on a classic riddle: Jayden has a dog-walking business. He has two plans. Plan 1 includes walking
    10·1 answer
  • The population of a certain city was 25,000 in 2010 and decreased by 4% each year afterwards. The population can be modeled by e
    5·1 answer
  • Please help I'm struggling​
    5·1 answer
  • 6) What is the equation of a line that passes<br> through (-1, -3) and has a slope of 2?
    6·1 answer
  • EXIT TICKET Complete on notebook paper. Put
    8·1 answer
  • 8. Lara invested a total of $1000 in two simple interest accounts. Account A pays
    11·1 answer
  • Based on these segment lengths, which group of segments cannot form a triangle? a. 12, 7, 8 b. 8, 7, 13 c. 1, 2, 3 d. 80, 140, 7
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!