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
Natalka [10]
3 years ago
13

Consider the polynomial p(s) = s2 + bs + c where b and c are real numbers. Show that all the roots of p(s) are both contained in

the open left half plane {s : s < 0} if and only if b > 0 and c > 0. Hint: use the quadratic formula.
Mathematics
2 answers:
hodyreva [135]3 years ago
7 0

Answer:

It is shown in the explanation

Step-by-step explanation:

p(s) = s² + bs + c

a = 1

b = b

c = c

We get Δ as follows

Δ = (b²-4*a*c) = b² - 4*1*c = b² - 4c > 0  ⇒   b² > 4c  ⇔ c > 0

s = (-b + √(b² - 4c))/2(1)

⇒   s₁ = (-b + √(b² - 4c))/2

s₂ = (-b - √(b² - 4c))/2(1)

⇒   s₂ = (-b - √(b² - 4c))/2

We have that -b < 0  ⇔ b > 0

then s₁ < 0 and s₂ < 0 ⇔ c > 0 and b > 0

Taya2010 [7]3 years ago
6 0

Answer:

For roots to lie on the left half plane, b ⊃ 0 and c ⊃0

Step-by-step explanation:

From quadratic formula, we have;

x = -b±√(b²-4ac)/2a

From the given expression p(s) = s² + bs + c,

x = s

a = 1

b = b

c = c

The quadratic formula can then be written as;

s =  -b±√(b²-4*1*c)/2*1

   =  -b±√(b²-4c)/2

s₁ =  -b+√(b²-4c)/2

s₂ =  -b±√(b²-4c)/2

From the equation above,

Sum of root = -b

Product of root = c

If both the root lie on left side of the s-plane, then sum of roots will be negative. Hence, -b ∠0. That is, b ⊃0

Also, the product root will be positive, c ⊃ 0

Hence, for roots to lie on the left half plane, b ⊃ 0 and c ⊃0

You might be interested in
A force of 22 pounds presses on a membrane. The average pressure on the membrane is 2.75 pounds per square inch (psi). What is t
Viefleur [7K]

Answer:

8 in^2.

Step-by-step explanation:

F = P * A

22 = 2.75 * A

A = 22/ 2.75

A = 8 in^2.

3 0
3 years ago
Read 2 more answers
Ann worked 14 hours and earned a total of $108.50.<br> How much did she earn per hour?
Delicious77 [7]

Answer:

108.50 divided by 14= 7.75

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Please answer this im going to fail Rewrite the fraction as a decimal.
ivolga24 [154]

Step-by-step explanation:

it ia 76.92 is the percentage for 10/13

8 0
3 years ago
Find x<br><br> A. X = 23<br> B. X = 31<br> C. X = 62<br> D. X = 118
Scorpion4ik [409]

Answer:

A

Step-by-step explanation:

6x-20= 118

6x= 118 + 20

6x = 138

x = 138/6

x= 23

8 0
2 years ago
Write an explicit formula for an, the nth term of the sequence 19,24,29
o-na [289]

Answer:

explicit formula for an, the nth term of the sequence 19,24,29

a_1=19 ; \ a_n=a_{n-1}+5

Step-by-step explanation:

We need to Write an explicit formula for an, the nth term of the sequence 19,24,29

In the sequence the First term a₁= 19

Common Difference d= 5

The Formula used for explicit formula is: a_1=First \ term ; \ a_n=a_{n-1}+d

Where d is common difference and n is nth term of sequence.

So, explicit formula for an, the nth term of the sequence 19,24,29

a_1=19 ; \ a_n=a_{n-1}+5

3 0
3 years ago
Other questions:
  • What is 1,562 divided. By 34
    11·1 answer
  • Suppose that m∠MKN = 55°. What is m∠MCN?<br> !please no absurd answers!
    13·2 answers
  • I need help with 14 and 16 please!!!!
    5·1 answer
  • The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 4 : 3. Terrence owns 36 models
    15·1 answer
  • I WILL GIVE BRAINLIEST!!
    8·2 answers
  • Mr. Green’s lawnmower holds 600milliliters of gasoline in the tank. He just filled his 6-liter gas can at the station. How many
    10·1 answer
  • There are 33 people at a meeting. Forty people had been asked to the meeting. What percent of the people asked to the meeting ar
    8·2 answers
  • I need help with this!!!!
    12·2 answers
  • Jeff bought 15 granola bars for $30. How much does it cost per granola bar? $
    9·2 answers
  • What is 32 divided by 526
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!