Which of the following is a complete set of solutions to 3x3+9x2−54x=0 ?(1 point)
Responses
no solutions
no solutions
0, 3, −6
0, 3, negative 6
0
0
0, −3, 6
0, negative 3 , 6
0, 3, -6
To find the solutions, we need to solve the equation 3x^3 + 9x^2 - 54x = 0.
Step 1: Factor out the common factor of x from the equation.
x(3x^2 + 9x - 54) = 0
Step 2: Solve the equation 3x^2 + 9x - 54 = 0.
Step 2a: Divide the equation by 3 to simplify it.
x^2 + 3x - 18 = 0
Step 2b: Factor the quadratic equation.
(x + 6)(x - 3) = 0
Step 3: Now solve for x in each of the factors.
For the first factor, x + 6 = 0, subtract 6 from both sides:
x = -6
For the second factor, x - 3 = 0, add 3 to both sides:
x = 3
Therefore, the complete set of solutions to the equation 3x^3 + 9x^2 - 54x = 0 is:
0, -6, and 3.
To find the complete set of solutions to the equation 3x^3 + 9x^2 - 54x = 0, we will solve the equation by factoring.
First, we can factor out x from the equation to get:
x(3x^2 + 9x - 54) = 0
Next, we can factor the quadratic expression (3x^2 + 9x - 54) by finding its roots:
We can start by dividing the expression by 3 to simplify the coefficients:
x(x^2 + 3x - 18) = 0
Now, we can factor the quadratic expression (x^2 + 3x - 18) by splitting the middle term:
x(x + 6)(x - 3) = 0
Therefore, the complete set of solutions to the equation 3x^3 + 9x^2 - 54x = 0 is 0, -6, and 3.