Question

I don’t know how to solve this. Can anyone help me get the answer and the work

Answer 1

{ -
`(2)/(3)`, 12 }

Explanation:

We can solve the equation by factoring it

3x² - 34x - 24 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × - 24 = - 72 and sum = - 34

The factors are - 36 and + 2

Use these factors to split the x- term

3x² - 36x + 2x - 24 = 0 ( factor the first/second and third/fourth terms )

3x(x - 12) + 2(x - 12) = 0 ← factor out (x - 12) from each term

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

Equate each factor to zero and solve for x

x - 12 = 0 ⇒ x = 12

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = -
`(2)/(3)`

Thus the solution set is { -
`(2)/(3)`, 12 }

Answer 2

If you have to check whether a number is a solution of a given equation, just plug that number in the equation and see if you get something true or false.

For example, the first option claims that -2 and 6 are solutions to the equation.

Let's check it! If we substitute
`x=-2` in the equation we get

`3(-2)^2-34(-2)-24 = 12+68-24=56 \\eq 0`

So, -2 isn't a solution to this equation. Let's check 6:

`3(6)^2-34(6)-24 = 108-204-24=-120 \\eq 0`

So, 6 isn't a solution either.

Keep going like this and you'll find the correct set of solutions.