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
Rama09 [41]
4 years ago
12

If α , β are roots of x2 + 5x + a =0 and 2α + 5β = -1 then α is equal to _____?

Mathematics
1 answer:
ELEN [110]4 years ago
3 0

9514 1404 393

Answer:

  -8

Step-by-step explanation:

If α and β are roots of x^2 +5x +a = 0, then we must have ...

  (x -α)(x -β) = x^2 +5x +a

  x^2 -(α+b)x +αβ = x^2 +5x +a

Then ...

  α + β = -5

Together with the other relation between the roots, we have a system of equations in α and β.

Using the above to write an expression for β, we get ...

  β = -α -5

Substituting this into the given relation, we have an equation for α:

  2α +5(-α -5) = -1

  -3α -25 = -1 . . . . . . eliminate parentheses

  -24 = 3α . . . . . . . . add 3α +1

  -8 = α

The root α is equal to -8.

You might be interested in
What are the solutions to 2(x-7)^2 = 32?
MariettaO [177]
2(x-7)^2 = 32\\
(x-7)^2=16\\
x-7=-4 \vee x-7=4\\
x=3 \vee x=11

3 0
3 years ago
2. In a given country, records show that of the registered voters, 45% are Democrats, 35% are Republicans, and 20% are independe
Kitty [74]

Answer:

P(R) = 0.14

P(I) = 0.16

P(D) = 0.315

Step-by-step explanation:

Let Democrat = D

Republican = R

Independent = I

If 45% are Democrats, 35% are Republicans, and 20% are independents, then

Total registered voters = 100

 In an election, 70% of the Democrats, 40% of the Republicans, and 80% of the independents voted in favor of a parks and recreation bond proposal. That is,

D = 0.7 × 45 = 31.5

R = 0.4 × 35 = 14

I = 0.8 × 20 = 16

 If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is

a Republican:

P(R) = 14 /100 = 0.14

an Independent

P(I) = 16/100 = 0.16

a Democrat

P(D) = 31.5/100 = 0.315

6 0
3 years ago
What is the lcm for 3/4and 1/2​
ioda

Answer:

1 1/2

Hope that helps!

Step-by-step explanation:

4 0
3 years ago
Find the value of x. If​ necessary, write your answer in simplest radical form. 30 x 25 x nothing ​(Simplify your answer. Type a
murzikaleks [220]

Answer:

x = 38.05

Step-by-step explanation:

Using the Pythagoras theorem to find x

x is the hypotenuse

The other sides are opposite and adjacent

x² = 30²+25²

x² = 900+625

x² = 1525

x = √1525

x = 39.05

4 0
3 years ago
Witch is greater 4 cups or 2 quarts
mario62 [17]
2 quarts because 4 cups only goes into 1 quart and 2 quarts is a greater number then 1 so 2 quarts
8 0
3 years ago
Other questions:
  • What is the median in the following number set?<br> 34, 71, 45, 21, 88, 53
    9·1 answer
  • A sum of money was shared between George and Benjamin in a ratio of 3:4. if the sum of money was $56.00, how much did George get
    12·1 answer
  • Corespondenta dintre numele si prenumele oamenilor defineste o functie ? justificati
    7·1 answer
  • What is the value of this inequality m-2&lt;-8 or m/8&gt;1?
    7·1 answer
  • Use synthetic division with the factor x + 1 to completely factor LaTeX: x^3+2x^2-5x-6x 3 + 2 x 2 − 5 x − 6.
    9·1 answer
  • I beg someone help.
    14·2 answers
  • Determine relationship b/t two triangles
    13·2 answers
  • What is the answer i need help
    7·1 answer
  • Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
    11·1 answer
  • A company is considering producing some new products. Based on past records, management believes that there is a 70% chance that
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!