Fully factored form: f(x) = (x − 3)(x + 3)[x − (2 − i)][x − (2 + i)] the function has real roots and imaginary roots.

2 real roots and 2 imaginary roots

f(x) = (x - 3)(x + 3 )(x-2 + i)(x - 2 - i)

(x - 3) and (x + 3) give real roots x = ± 3

(x - 2 + i)(x - 2 - i) give 2 imaginary roots x = 2 ± i

Real roots:

Imaginary roots:

Step-by-step explanation:

We have been given fully form of a polynomial: . We are asked to find the real and imaginary roots of our given polynomial.

We can see that our given polynomial has two real and two imaginary roots.

Upon equating our given factor to 0 we will get roots of our given polynomial as:

Therefore, are real roots of our given polynomial.

Therefore, are imaginary roots of our given polynomial.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

8 2/3 is the answer

step-by-step explanation: just use a calculator