x cube plus kx plus 9=0
I took it as: x^3+kx+9=0
I answered:
If so.........
x^3+kx+9=0
Subtract 9 from both sides (Somenoe correct me if I'm wrong, please) which looks like:
x^3+kx+9-9=0-9
Now the best part.... finding variables
x^3+kx=9
x^3+(k•x)=9
Hmmm...
x^3= (x•x•x)
x•x•x•x+k=9
I'm not sure how to proceed....
How would I do this? I want to learn while I'm answering questions...
Thank you!
- Anonymous
To solve the equation x^3 + kx + 9 = 0, you can use algebraic techniques such as factoring or using the rational root theorem. Let's explore the steps further:
Step 1: Subtract 9 from both sides of the equation to isolate the terms involving x:
x^3 + kx = -9
Step 2: Next, we want to express x^3 + kx as a product of factors. One way to do this is by factoring out the greatest common factor of x:
x(x^2 + k) = -9
Step 3: Now, we have two cases to consider:
Case 1: If x = 0, then the equation becomes:
0(x^2 + k) = -9
0 = -9
This is not a valid solution, so we move to the second case.
Case 2: If x ≠ 0, then we can divide both sides of the equation by x:
x^2 + k = -9/x
Step 4: At this point, the equation has become a quadratic equation in terms of x^2. To solve for x^2, we can use various methods like factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x^2 = (-9/x) - k
Applying the quadratic formula:
x^2 = (-9/x) - k
x = [-(9/x) ± sqrt((9/x)^2 - 4k)] / 2
Simplifying the expression under the square root:
x = [-(9/x) ± sqrt((81/x^2) - 4k)] / 2
Step 5: Finally, we have the potential solutions for x. To determine if they are valid solutions, substitute them back into the original equation and check if it satisfies the equation x^3 + kx + 9 = 0.
Remember, this is just one method to approach this equation. Depending on the values of k and other factors, different methods might be more suitable. It's always helpful to have a good understanding of algebraic techniques and practice with solving various types of equations.