Solving Equation: x^5 + k^2x = 0

[Atomised]

Homework Statement

I am asked to solve the following equation, giving answer in terms of k

Homework Equations

$$x^5 + k^2x = 0$$

The Attempt at a Solution

The answer is apparently 0. What is 0. Not even sure what that means.

I would have thought: divide through by x to obtain

$$k^2 = -x^4$$ →

$$ k=x^2i $$ ?

 

[paisiello2]

You solved for k. I think you were supposed to solve for x.

I agree with you that there is more than one root.

 

[SammyS]

Homework Statement

I am asked to solve the following equation, giving answer in terms of k

Homework Equations

$$x^5 + k^2x = 0$$

The Attempt at a Solution

The answer is apparently 0. What is 0. Not even sure what that means.

I would have thought: divide through by x to obtain

$$k^2 = -x^4$$ →

$$ k=x^2i $$ ?

Dividing both sides of an equation by anything except zero, gives you an equivalent equation.

You can divide by x, as long as it's not equal to zero.

What if x is zero?

Evaluate that case another way, for instance, by plugging zero in for x.​

 

[Mark44]

Homework Statement

I am asked to solve the following equation, giving answer in terms of k

Homework Equations

$$x^5 + k^2x = 0$$

The Attempt at a Solution

The answer is apparently 0. What is 0. Not even sure what that means.

The "answer" is not zero. Your answer should be in the form of equations that start with "x = ..."

One of the solutions is x = 0, but there is another. Factoring the left side would be helpful.

 

[Ray Vickson]

Homework Statement

I am asked to solve the following equation, giving answer in terms of k

Homework Equations

$$x^5 + k^2x = 0$$

The Attempt at a Solution

The answer is apparently 0. What is 0. Not even sure what that means.

I would have thought: divide through by x to obtain

$$k^2 = -x^4$$ →

$$ k=x^2i $$ ?

You have committed the worst sin in mathematics, viz., dividing by x before checking that it is allowed. If x = 0 you cannot do any such division---but in that case, you don't need to anyway. If x ≠ 0 then---and only then---can you divide both sides by x.

 

[Atomised]

Thanks Mark & Ray for these lessons - a great help in learning to think properly.