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 [tex]x=-2[/tex] in the equation we get
[tex]3(-2)^2-34(-2)-24 = 12+68-24=56 \neq 0[/tex]
So, -2 isn't a solution to this equation. Let's check 6:
[tex]3(6)^2-34(6)-24 = 108-204-24=-120 \neq 0[/tex]
So, 6 isn't a solution either.
Keep going like this and you'll find the correct set of solutions.
Answer:
{ - [tex]\frac{2}{3}[/tex], 12 }
Step-by-step 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 = - [tex]\frac{2}{3}[/tex]
Thus the solution set is { - [tex]\frac{2}{3}[/tex], 12 }
