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
notsponge [240]
2 years ago
7

The roots of the quadratic equation $z^2 + bz + c = 0$ are $-7 + 2i$ and $-7 - 2i$. What is $b+c$?

Mathematics
1 answer:
Alexxx [7]2 years ago
8 0

Answer:

67

Step-by-step explanation: Given the quadratic equation $z^2 + bz + c = 0$, Vieta's formulas tell us the sum of the roots is $-b$, and the product of the roots is $c$. Thus,

\[-b = (-7 + 2i) + (-7 - 2i) = -14,\]so $b = 14.$

Also,

\[c = (-7 + 2i)(-7 - 2i) = (-7)^2 - (2i)^2 = 49 + 4 = 53.\]Therefore, we have $b+c = \boxed{67}$.

There are many other solutions to this problem. You might have started with the factored form $(z - (-7 + 2i))(z - (-7 - 2i)),$ or even thought about the quadratic formula.

This is the aops answer :)

You might be interested in
A coin is tossed 5 times and a tail is the outcome each time. what is the probability of getting a tail on the sixth throw
Norma-Jean [14]
I believe it would be
1/5
5 0
3 years ago
A(-5,-4) ——> A’ is a glide reflection where the translation is (x,y)—->(x+6,y), and the line of reflection is y=3. What ar
Nastasia [14]

Solution:

The Point in the coordinate plane is A(-5,-4).

Perpendicular or shortest Distance from line y=3 that is (-5,3) to point (-5,-4) is

=\sqrt{(-5+5)^2+(3+4)^2}\\\\=7

When it is reflected through the line, y=3, the coordinate of point A (-5,-4) changes to (-5,3+7)= B(-5,10).

Now, the Point B is translated by the rule , (x,y)—->(x+6,y),

So,the point B is translated to, (-5+6,10)=(1,10)

Option C: (1,10) is the glide reflection of point A(-5,-4).

8 0
3 years ago
Read 2 more answers
HELP PLSSSSS!!!!! I WILL Give Brainlyist
Basile [38]

Answer:

\frac{5}{6}

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What number is 70% of 120?please give the equation with x
MA_775_DIABLO [31]
You can set up this equation as:
x = 0.7(120)

Because remember, 70% is equal to 0.7 and x represents the unknown value. So, let's just solve it:
x = 0.7(120)=84

So, 70% of 120 is 84.
7 0
3 years ago
The daltons completed 30% of their 2140-mile trip the first day
Ugo [173]
To figure out how many miles the Daltons traveled the first day you times 2140 miles and 30 percent.
So 2140 x .30 = 642
They traveled 642 miles the first day.

To figure out how many miles they still have to travel you subtract your original miles (2140) from how many miles they have already traveled (642).
So 2140 - 642 = 1498
They have 1498 miles to still travel.
4 0
2 years ago
Read 2 more answers
Other questions:
  • 2 doctors is what percent of 25 doctors
    14·1 answer
  • The radius of a circle is 5 1 2 cm. what is the circle's circumference in terms of p ?
    5·1 answer
  • M(p + p); use m = 2, and p = 3
    7·1 answer
  • Look at the figure. Complete the statement and justify your answer.UT is congruent to _____ is congruent to YX.
    13·2 answers
  • Pls help I will give brainliest
    9·1 answer
  • For all positive integers n, let *n* equal the greatest prime number that is a divisor of n. What does *10*/*12* equal?
    12·1 answer
  • On a coordinate plane, a point is at (1, 2) and (5, 2). Find the distance between (1, 2) and (5, 2). The points lie in the same
    7·2 answers
  • Which figure has rotational symmetry but no line symmetry?
    12·1 answer
  • Please help !!! ASAP
    13·2 answers
  • For friends went to a restaurant in bought Two large pizzas and if each pay 5.25 how much was each pizza
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!