F(x) = 3x^2+12x+5f(x)=3x 2 +12x+5f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 12, x, plus, 5 What is the value of the discriminant of fff? How many distinct real number zeros does f(x)f(x)f, left parenthesis, x, right parenthesis have?

Discriminant = 84

The polynomial has two real distinct roots

Step-by-step explanation:

Given:

To find: discriminant of the given function and number of distinct real zeros

Solution:

For a polynomial , discriminant is given by

If , then the polynomial has two real and distinct roots.

If then the polynomial has two real and equal roots.

If D<0 then roots are not real.

Here, in

a = 3, b = 12 and c = 5

As D > 0, the polynomial has two real distinct roots.

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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

the answer

b. they are parallel and will never intersect.