Which of the following equations have complex roots?
a. x^2=−7x−2
b. x^2+3x+9=0
c. x^2=5x−1
d. x^2=−7x+2

B

Step-by-step explanation:

A:

Completing the square:  (x+ 7/2)^2 = -2 + 49/4 = 41/4, in the next step you'll be square rooting a positive number so it'll have real roots.

B:

Completing the square:  (x+3/2)^2 = -9 + 9/4 = -27/4, you'll next be square rooting a negative number, so it'll have complex roots

C:

Completing the square:  (x-5/2)^2 = -1 + 25/4 = 21/4, next you'll square root a positive number, so real roots

D:

Completing the square: (x+7/2)^2 = 2 + 49/4 = 57/4, square root a positive number, so real roots.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

step-by-step explanation:

one day the were 5 ducks, and their king told them to multiply their kingdom. so each went their own seperate way and met 4 other ducks on their journey.

when the ducks returned to their kingdom, it was discovered that there were 5 groups of 5 ducks. when the kind counted the number of ducks in total (including the ones he sent out earlier) he counted 25.

therefore 5 times 5 is 25.

the end. : )