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 ..

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

1/4 because there is 4 grades.