Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2? f(x) = 2(x + 7)(x + 5)(x – 2) f(x) = 2(x – 7)(x – 5)(x + 2) f(x) = (x + 7)(x + 5)(x + 5)(x – 2) f(x) = (x – 7)(x – 5)(x – 5)(x + 2)

Option 4

Step-by-step explanation:

We can check the options one by one.

for f(x)=2(x+7)(x+5)(x-2)

We can see that

Putting the factors one by one equal to zero will give us:

The above roots are not according to the given requirements so it is not the correct answer.

For f(x)=2(x-7)(x-5)(x+2)

The roots will be:

The roots are not according to the requirements of the question as the multiplicity of 5 is not two

For f(x) = (x + 7)(x + 5)(x + 5)(x – 2)

The roots will be:

Again the roots are not according to given requirements

For f(x) = (x – 7)(x – 5)(x – 5)(x + 2)

For finding the roots, put the function equal to zero

We can see that the roots are -2, 7 and 5 and the root 5 has multiplicity of two.

For leading co-efficient the factors will be multiplied:

We can see that the leading co-efficient is 1.

So option 4 is the correct answer ..

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

k

step-by-step explanation:

domit