how do you solve this?

Question

3x^2 - 34x - 24 = 0

and these problems?
Five people have volunteered to work on an awards dinner at Madison High School. How many different committees of four can be formed from the five people?

if TAN A = 6/4 what is A?

if TAN A = 6/4 what is A?

if TAN A = 6/4 what is A?

Answer 1

3x² - 34x - 24 = 0

The middle term is - 34x

Find the sum of the middle term

Multiply the first term 3 times the last term 24 equals - 72 and factor.

Factors of - 72 are

1 x - 72
2 x - 36. . .←. .Use the factors
3 x - 24
4 x - 18
6 x - 12
8 x - 9

- 36x and + 2x satisfy the sum of the middle term

Insert - 36x and + 2x into the equation

3x² - 34x - 24 = 0

3x² - 36x + 32x = 24 = 0

Group factor

(3x² - 36x) + (2x - 24) = 0

3x(x - 12) + 2(x - 12) = 0

(3x + 2)(x - 12) = 0

- - - - - - - -s-

Answer 2

You can factor it...

3x^2 - 34x - 24 = 0
3x^2 - 36x + 2x - 24 = 0
3x(x - 12) + 2(x - 12) = 0
(3x + 2)(x - 12) = 0
x = 12, -2/3

5 volunteer groups can be formed because each group has one person missing, since there are 5 possible people that can be missing, there are 5 groups.

Answer 3

There are five volunteers. Each committee excludes one volunteer, so five different committees are possible.
--------------
3x² - 34x - 24 = 0
x² - (34/3)x - 8 = 0
x² - (34/3)x = 8

Complete the square:
x² - (34/3)x + (17/3)² = 8 + (17/3)²
(x - 17/3)² = 8+289/9
= 361/9


Take square root of both sides:
x - 17/3 = ±√(361/9)
= ±√361/√9
= ±19/3
x = 17/3±19/3
x₊ = 36/3 = 12
x₋ = -2/3

Answer 4

You can try to factor it or use the quadratic equation. If you choose to try to factor it you would start off trying something like (x+a)(3x+b) since the leading coefficient is 3.
Since ab=-24 a and b will be of different signs. Now just try values to see what works. Eventually you will get:

(x-12)(3x+2)
x = 12 or x = -2/3

Answer 5

Factor the equation:
(3x + 2) (x - 12) = 0

Set both equal to 0 and solve:
If
3x + 2 = 0

Then
3x = -2
x = -2/3

-or-

If
x - 12 = 0

Then
x = 12

So x has 2 solutions: (-2/3, 12)

Answer 6

= (3x+2)(x-12) = 0
x = 12 and x = -2/3