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
worty [1.4K]
3 years ago
5

The expression $x^2 15x 54$ can be written as $(x a)(x b),$ and the expression $x^2 - 17x 72$ written as $(x - b)(x - c)$, where

$a$, $b$, and $c$ are integers. What is the value of $a b c$?
Mathematics
2 answers:
Natalka [10]3 years ago
7 0

Answer: a=6 b=9 c=8

Step-by-step explanation:

The problem consists of finding the roots of the quadratic equations:

x^2+15x+54=0\\

x^2-17x+72=0\\

The roots can be found with the following equation for solving quadratic equations:

x_{12}=\frac{-B\pm\sqrt{B^2-4AC}}{2A}  for equation: Ax^2+Bx+C=0

After solving the equations you can write the result as:

x^2+15x+54=(x+6)(x+9)\\

x^2-17x+72=(x-9)(x-8)

Naya [18.7K]3 years ago
7 0

Answer:

b = 9

a = 6

c= 8

Therefore, a,b,c = 6,9,8

Question:

The expression $x^2 - 15x - 54$ can be written as $(x-a)(x-b),$ and the expression $x^2 - 17x + 72$ written as $(x - b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a b c$?

Step-by-step explanation:

To determine the values of a,b and c.

We need factorize the two equations.

i) x^2 -15x +54

x^2 -6x -9x +54

x(x-6) -9(x-6)

=(x-6)(x-9)

ii) x^2 -17x +72

x^2 -9x -8x +72

x(x-9) -8(x-9)

=(x-9)(x-8)

From the question:

Comparing

(x-a)(x-b) to (x-6)(x-9)

And

(x-b)(x-c) to (x-9)(x-8)

We can see that b is common in the two cases and also 9 is common in the two factorised equations.

So,

b = 9

a = 6

c= 8

Therefore, a,b,c = 6,9,8

You might be interested in
What is the points for C on the graph?
qaws [65]
The points for C is (12, 10.5)
5 0
2 years ago
Read 2 more answers
Help with this please
Svet_ta [14]
The answer to the question is D
4 0
3 years ago
Read 2 more answers
A movie theater seating is arranged with 15 seats in the front row, 14 seats in the middle row, and 26 seats in the back row. Th
Kryger [21]

Answer:

3/11

Step-by-step explanation:

i did this question it 3/11

6 0
2 years ago
How do I solve for A??
Alja [10]
1)Add up the numbers and variables.
2) Triangles equal 180 degrees.
3)Subtract the total of the numbers and 180.
4) Then divide by the variable.

X= -10
3 0
3 years ago
Please answer both A and B
Anton [14]
A) -53°C (airplane fuel)
b) butter
5 0
3 years ago
Read 2 more answers
Other questions:
  • LOTS OF POINTS!
    13·1 answer
  • Explain why there is a discrepancy between them if there is any?
    12·1 answer
  • You are an engineer for a company that produces shipping boxes. The boxes that are made on one machine are all in the shape of a
    7·1 answer
  • Find the slope, if it exists of the line containing the points (-4, 0) and (-5,-3)
    5·2 answers
  • please help don't know how to do this A stone is an English measure of weight. There is 14 lb in 1 stone and 2.2 lb in 1 kg. A c
    14·1 answer
  • Maria spins a penny 100 times and it lands head side up 62 times. Explain why Maria's experimental probability may be different
    11·1 answer
  • What is the value of 3 ^ -3
    14·1 answer
  • The rule T 5, -0.5° Ro, 1800(x, ) is applied to FGH to
    13·1 answer
  • Which point on the graph best represents the location of left parenthesis minus 4.5 comma space minus 7 right parenthesis ?
    11·2 answers
  • REALLY EASY, REALLY NEED HELP
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!