Find the discriminant of the quadratic equation x2 + 10x + 24 = 0 and use it to determine the number and types of solutions.
b2 - 4ac

2 real solutions since the discriminant is 4 and is greater than 0.

Furthermore, since 4 is a perfect square then the answers are also going to be rational.

You will have 2 real rational solutions.

Step-by-step explanation:

Compare the following to determine the values for :

.

.

Now we are going to compute:

So the discriminant is 4.

Here is the thing about discriminant (D) assuming are real:

If D=0, then you have one real solution.

If D<0, then you have no real solution.

If D>0, then you have two real solutions.

Our D (discriminant) is 4 and 4 is positive or >0, so we have two real solutions.

There is another thing we can tell about this particular discriminant.

Since it is a perfect square, then we know the answers will also be rational.

d

gimmee one of those gold crowns!

~coco

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~