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
BlackZzzverrR [31]
3 years ago
14

What is the product of all constants $k$ such that the quadratic $x^2 + kx +15$ can be factored in the form $(x+a)(x+b)$, where

$a$ and $b$ are integers?
Mathematics
1 answer:
Setler79 [48]3 years ago
6 0

Answer:

k=-16,k=-8,k=8,k=16

Step-by-step explanation:

We are given quadratic equations as

x^2+kx+15

and it can be factored as

=(x+a)(x+b)

now, we can multiply factor term

(x+a)(x+b)=x^2+(a+b)x+ab

now, we can compare

x^2+(a+b)x+ab=x^2+kx+15

so, we get

k=a+b

ab=15

we are given that

'a' and 'b' are integers

so, we can find all possible factors

15=(-1\times -15),(1\times 15)

15=(-3\times -5),(3\times 5)

so, we can find k

At (-1\times -15):

k=a+b

we can plug values

k=-1-15

k=-16

At (1\times 15):

k=a+b

we can plug values

k=1+15

k=16

At (-3\times -5):

k=a+b

we can plug values

k=-3-5

k=-8

At (3\times 5):

k=a+b

we can plug values

k=3+5

k=8

So, values of k are

k=-16,k=-8,k=8,k=16

You might be interested in
Midpoint of the line segment (-1,6), (-6,5)
zepelin [54]
The answer is:

(-7/2 , 11/2)

5 0
2 years ago
How much would $400 invested at 9% interest compounded continuously be worth after 3 years? Round your answer to the nearest cen
adell [148]
<span>In 3 years, you will have $523.97 
</span><span>continuously = daily</span>
3 0
3 years ago
Read 2 more answers
Linda and Colleen both leave the library at the same time, but in opposite direction. If Colleen travels 8mph faster than Linda
pshichka [43]
X - Linda's speed
(x+8 )- Colleen's speed

8x - Linda's distance for 8 h
8(x+8) = 8x+64  - Colleen's distance for 8 h

8x + 8x + 64 = 176 - distance between Colleen and Linda after 8 h


8x + 8x + 64 = 176 
16x +64 = 176
16x = 176 - 64
16x = 112
x= 7 mph Linda's speed
x+8
= 7+8 = 15 mph Colleen's speed
8 0
3 years ago
What does this equal =
lana [24]
The equation is y=mx+c, in which m is the slope(1/2), c is the y intercept (5), and x is the x intercept (0)
 thus, the equation is:
 y=(1/2)(0)+5
y=5

hope it helps!
7 0
3 years ago
What is the area of this square?
shepuryov [24]
Area = 40x40 = 1600<span>km²

answer 

</span><span>D.
1,600 km²</span>
5 0
3 years ago
Read 2 more answers
Other questions:
  • If you have 6 oranges and eat 3 2/3 how many do you have left
    15·2 answers
  • Graph and label Point H at 1.5 , negative 6 thirds
    6·1 answer
  • ∆ABC is plotted on a coordinate plane. If ∆ABC rotates 90° clockwise around point C, what are the coordinates of A'?
    7·1 answer
  • Find the coordinates of the midpoint of the segment whose endpoints are H(5, 13) and K(7, 5). (12, 18)
    15·1 answer
  • -6*4/2*3-15 help please
    6·2 answers
  • 36 ft 41 1/2 ft find the area
    13·1 answer
  • Which expressions are perfect cubes?<br> -1,000<br> 0 2721<br> 343p<br> O n30<br> ebo...<br> -1
    14·1 answer
  • -3x-5&lt;10 Equations ​
    15·1 answer
  • Subtract-a^2-5ab+3ab^2 from 3a^2-2ab+3b2
    8·2 answers
  • What is the average of 79.3, 64.3, 103.4, 46.4, 46.2
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!