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
dem82 [27]
3 years ago
10

Find the zeros for each function

Mathematics
1 answer:
iogann1982 [59]3 years ago
5 0

9514 1404 393

Answer:

  1. zeros are -10, and -1 (multiplicity 2)
  2. zeros are {-3, -2, 1, 3}

Step-by-step explanation:

For higher-degree polynomials I find it extremely useful to use a graphing calculator to find the zeros.

The usual approaches are ...

  • use the rational root theorem
  • try values of x=±1
  • narrow the search using Descartes' rule of signs
  • estimate maximum or minimum root values

__

1. Rational roots will be factors of 10, so ±1, ±2, ±5, or ±10. The signs are all positive, so there are no positive real roots. The sum of odd-degree coefficients is the same as the sum of even-degree coefficients, so -1 is one of the roots. Removing that using synthetic division gives you ...

   f(x) = (x +1)(x^2 +11 +10)

The quadratic (more or less obviously) factors as (x+1)(x+10), so the complete factorization is ...

  f(x) = (x +1)^2(x +10)

and the zeros are {-10, -1, -1}.

__

2. Rational roots will be factors of 18, so will be ±1, ±2, ±3, ±6, ±9, ±18. The sum of coefficients is 0, so x=1 is a root. The rule of signs tells you that there are 2 positive real roots, so there is one more positive real root. Synthetic division tells you the factoring so far is ...

  f(x) = (x -1)(x^3 +2x^2 -9x -18)

We note that the first two coefficients have the same ratio as the last two, so we can factor by grouping.

  x^3 +2x^2 -9x -18 = x^2(x +2) -9(x +2) = (x^2 -9)(x +2)

Factoring the difference of squares gives you the complete factorization, hence all of the roots. (The zeros are the values of x that make the factors zero.)

  f(x) = (x -1)(x +2)(x -3)(x +3)

The zeros are {-3, -2, 1, 3}.

You might be interested in
Solve this equation, and show work. worth 40 points.
krek1111 [17]

Answer:

b = - 3

Step-by-step explanation:

Please see the attachment below of the following work.

Thanks! Can I have BRAINLIEST please?

Hope this helps!

4 0
3 years ago
Read 2 more answers
Find the value of the variables, giving brief reasons for your answer:​
Pavlova-9 [17]

Answer:

a = 70°

b = 80°

Step-by-step explanation:

Angles on a straight line add up to 180°

⇒ a + 110 = 180

⇒ a = 180 - 110

⇒ a = 70°

The sum of the interior angles of a quadrilateral is 360°

⇒ a + b + 130 + 80 = 360

⇒ 70 + b + 130 + 80 = 360

⇒ b + 280 = 360

⇒ b = 360 - 280

⇒ b = 80°

3 0
2 years ago
Write a function to give arbitrary probabilities (totalling 100%) to each face of a six-sided die.
Andre45 [30]
P(A) = N/0
where P(A) equals Probability of any event occurring
N is the Number of ways an event can occur and
0 is the total number of possible Outcomes

P(A) = 1/6

Plainly the probability of rolling a six with a single six-sided dice is one event in which it lands with six uppermost, divided by six possible outcomes from a single throw, or one sixth (16.66 per cent).
7 0
3 years ago
Can you help me with a and b​
tigry1 [53]

Answer:

bro these college story problems getting deep

Step-by-step explanation:

3 0
2 years ago
A book is opened, and the PRODUCT of the two visible page numbers is found to be 306. The equation which correctly represents th
nexus9112 [7]
The answer is C, x^2 + x = 306
3 0
3 years ago
Read 2 more answers
Other questions:
  • If avogadro's number of pennies is divided equally among the 250. million men, women, and children in the united states, how man
    7·1 answer
  • 14tx=46;x=32 what's the answer?​
    8·2 answers
  • Which of the following fractions is equivalent to the repeating decimal 0.55555555555...?
    9·2 answers
  • Serenity used an iPhone to take a photo of the flagpole. In the photo, the flag pole has a height of 3 inches. If the photo used
    10·2 answers
  • Please help me with questions 30-33
    10·1 answer
  • The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.2 years, with a standard devia
    10·1 answer
  • How many times geater is one hour than one minute
    5·2 answers
  • Claire makes a salary of of $37,500.00. She gets paid quarterly . How much does she get paid each pay period?
    13·1 answer
  • Which of the following equations represents the line with a slope of -7/4 and a y-intercept of -11?
    6·1 answer
  • What’s the slope? <br> 50 points!! Please help
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!