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
Tom [10]
2 years ago
14

Given a leading coefficient of 8, polynomial roots of 1 & 2, and the known point on the graph (4,5). Write an equation that

will find the
missing 3rd root (r). You do not have to solve the problem. See the example "Find the Missing Root - Interesting Twist" if you need help.


_=_(_-1)(_-2)(_-_)
Mathematics
1 answer:
m_a_m_a [10]2 years ago
8 0

Given:

The leading coefficient of a polynomial is 8.

Polynomial roots are 1 and 2.

The graph passes through the point (4,5).

To find:

The 3rd root and the equation of the polynomial.

Solution:

The factor form of a polynomial is:

y=a(x-c_1)(x-c_2)...(x-c_n)

Where, a is a constant and c_1,c_2,...,c_n are the roots of the polynomial.

Polynomial roots are 1 and 2. So, (x-1) and (x-2) are the factors of the polynomial.

Let the third root of the polynomial by c, then (x-c) is a factor of the polynomial.

The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:

y=8(x-1)(x-2)(x-c)

The graph passes through the point (4,5). Putting x=4,y=5, we get

5=8(4-1)(4-2)(4-c)

5=8(3)(2)(4-c)

5=48(4-c)

Divide both sides by 48.

\dfrac{5}{48}=4-c

c=4-\dfrac{5}{48}

c=\dfrac{192-5}{48}

c=\dfrac{187}{48}

Therefore, the 3rd root on the polynomial is \dfrac{187}{48}.

You might be interested in
14 POINTS 7x - 3 = 18
Svetlanka [38]
Subtract 3 first so it would be 7x=15
then divide by 7 so x would be approximately 2.14
5 0
3 years ago
Read 2 more answers
HELP PICTURE IS SHOWN
Marrrta [24]
C hope it helps .....................
6 0
3 years ago
One tile yellow, 2 tiles blue, and 3 tiles are purple. What fraction of tiles are yellow or purple
Harlamova29_29 [7]
3 plus 1 equals 4 so its 4/6. When you simplify it the answer is 2/3
3 0
3 years ago
(0,0), (1,5), (2,20), (3,45), (4,80) what's the rule?
yanalaym [24]
Hmm, seems to multiply by 5
wait, no

first is multiply by 5
2nd is multiply by 10
3rd is multiply by 15
4th is multiply by 20
seems to be

f(x)=x(5x) or f(x)=5x^2
the rule is square the input then multiply by 5
5 0
2 years ago
What is the coefficient of the variable in the expression 6-4x-8x+2
Daniel [21]

I think the trick is to add the two middle terms together.  (And the 2 end terms).

8 - 12x

The variable is x. The coefficient is - 12.

8 is a constant.

The coefficient always goes with a variable.

3x^2 + 2x + 5

Nothing can be combined.  The leading coefficient is 3 (which goes with the greatest power of the variable x^2 in this case) and the other coefficient is 2. 5 is a constant.  

6 0
3 years ago
Other questions:
  • X^2+4x+3 factor each polynomial
    8·1 answer
  • 2 friends share 3 fruit bars equally. How much does each friend get?
    5·2 answers
  • What cross section results when you cut a cylinder perpendicular to its base?
    13·1 answer
  • Fareed wants to add 1/4 +5/8 Add the fractions by using the giant one to create a common denominator
    12·1 answer
  • What is the base area of a cube prisim 5mm
    13·1 answer
  • a television set was sold during a clearance sale for dollar 299.00the television was sold at a discount of 70 percent, what was
    13·1 answer
  • How many pounds of candy worth 70 cents a pound must be mixed with 30 pounds of candy worth 90 cents a pound to produce a mixtur
    11·1 answer
  • Find the solution to the syster<br> y = 2x = 5<br> y = X - 2
    9·1 answer
  • Plss help for what ever u want
    10·1 answer
  • Please help me, this is due today and I'm very confused.. :l
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!