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
belka [17]
3 years ago
8

If x = 1 is a common root of ax² +ax + 2 = 0 and x² + x + b = 0 , then ab =

Mathematics
1 answer:
vodka [1.7K]3 years ago
6 0

Answer:

ab = 2

Step-by-step explanation:

Given equations

ax² +ax + 2 = 0

x² + x + b = 0

root of both the equation

x= 1

then we can plug in x = 1 in both the equation

ax² +ax + 2 = 0                        x² + x + b = 0

a*1² +a*1 + 2 = 0                        1² + 1 + b = 0

a +a + 2 = 0                                 1 + 1 + b = 0

2a + 2 = 0                                    2 + b = 0

2a = -  2                                         b = -2

a = -2/2 = -1

Thus,

a = -1

b = -2

a*b = -1*-2 = 2

ab = 2

You might be interested in
What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix? Enter the equation in the box.
antiseptic1488 [7]

Check the picture below.  So the parabola looks more or less like so.

let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.

Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as  you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.

\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5

6 0
3 years ago
After 1 minute, a submarine had descended to −280 feet. After 9 minutes, the submarine had descended to −360 feet. Assuming a li
adelina 88 [10]

Answer:

the answer is 640

Step-by-step explanation:

-280-360 = 640

d(t)=-360

= 360*d*t

4 0
2 years ago
Two brothers have ages that are consecutive odd integers. The product of their ages is 38 less than the older brother's age squa
Lemur [1.5K]

answer = the elder bother is 17 and the younger one is 15

constructive odd integers= 15 and 17

17×15= 255

255+38 = 293

Square root of 293 = 17

5 0
3 years ago
What is the value of p in the equation shown? <br> 3<br> p =-0.027
Art [367]

Answer:

According to the question,

3p=-0.027

By transposing '3' to the RHS, we get

p=0.027/3

=  p=-0.009

So in this question p=-0.009

4 0
3 years ago
Ok I have math hw , and we are doing solving systems of linear equations by graphing and i can’t find where these two lines inte
likoan [24]

Answer:

Line 1, y=-3, x=-3

Line 2, y=2, x=1 1/3

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Cos(a) 63/65 to find sin(a) and tan(a)
    13·2 answers
  • LetA,B,CandDbe the following sets:A={red, blue, green, purple}B={red, red, green}C={red,{green}, red,{red, green},{green, green,
    8·1 answer
  • A local screen-printing company sells T-shirts at various prices, in dollars, depending upon how many T-shirts are bought at
    9·2 answers
  • What is the predicted profit when the number of items made (x) is 2,500, and the number of stores stocking the product (x2) is 5
    12·1 answer
  • On a field trip, there are 8 adults and 24 students. What is the ratio of students to the total number of people on the field tr
    8·2 answers
  • 1. Simplify the following expression. *<br> 11/15 - 1/6
    5·2 answers
  • Write an equation of the line below.
    11·1 answer
  • Help me ;-;<br><br> Find (2)(‐3)
    14·1 answer
  • Pls explain pls this will help alot
    6·1 answer
  • Find the value of P.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!