The roots for the given equation are -8 and 3.
Step-by-step explanation:
The first thing we must do in order to find the roots is factor the equation. We can do this by first multiplying the first and last term together. Then, we find the factors of that product that multiply together to that product but also adds together to get the middle term in the equation.
x² * -24 = -24x²
-24x² = 8x * -3x
Now, we write our new equation by replacing 5x with 8x - 3x.
x² + 8x - 3x - 24
Group the first and second terms together and also group the last two terms together.
(x² + 8x) + (-3x - 24)
Factor each parentheses. You will know that you factored them correctly when the two terms in the final parentheses are the same.
x(x + 8) -3(x + 8)
Since the two terms in the parentheses are the same, hen we have correctly factored out the equation. Now, we form the equation so we can find the roots.
(x - 3)(x + 8)
Now, equal each term in the parentheses to zero.
x - 3 = 0
x + 8 = 0
Now, solve for x in each equation. The final answer for each equation will be our roots. The roots are the values of x in a quadratic equation.
x = 3
x = -8
So, the roots of this equation are {-8, 3}
