not sure i'm doing this right

[homeschool girl]

the question is

In the quadratic equation

solve for

in terms of

.

and my answer is

[MATH]x^2 + \left(k-\frac{1}{k}\right)x - 1 = 0[/MATH]First we distribute
[MATH]x^2 + kx-\frac{1}{k}x - 1 = 0[/MATH]and factor
[MATH]\left(x-\frac{1}{k}\right)\left(x+k\right)= 0[/MATH]
either [MATH]\left(x-\frac{1}{k}\right)= 0[/MATH] or [MATH]\left(x+k\right)= 0.[/MATH]
we find the factors:
[MATH]x-\frac{1}{k}= 0[/MATH]
[MATH]x= \frac{1}{k}[/MATH]

[MATH]x+k= 0[/MATH][MATH]x=-k[/MATH]
so [MATH]x=\boxed{-k,\frac{1}{k}}[/MATH]
but I'm not sure that's right

 

[tkhunny]

Two things:

1) I was a little disappointed in your presentation because you did not show HOW you managed to factor the expression.
2) What if k = 0?

Very good work. Well written and easy to follow. And thanks for learning enough LaTeX!

 

[MarkFL]

I love how quickly you've picked up the use of \(\LaTeX\)!

Your works looks great to me. If you are unsure if the roots you've found are correct, you can always substitute for \(x\) into the original equation and make sure the roots make the expression equal to zero.

 

[lev888]

Just plug in each root and check.

 

[Steven G]

Why did you distribute.
Nice work otherwise.
As mentioned, you can check your solutions but substituting back.