Determine k and solve the equation x^3 -kx^2 + 20x +12 = 0.

Thanks

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- Aug 30th 2007, 06:43 PMMr_Greensolving an equation
Determine k and solve the equation x^3 -kx^2 + 20x +12 = 0.

Thanks - Aug 30th 2007, 06:45 PMThePerfectHacker
- Aug 30th 2007, 06:47 PMMr_Green
my bad...

Determine k and solve the equation x^3 - kx^2 +20x + 12 = 0, if one of its zeros is the triple of another. - Aug 30th 2007, 07:03 PMThePerfectHacker
Let be zero's (counting multiplicity).

One of its zeros, say , is triple of another, say . Thus, .

Thus, we have that,

Thus,

Now we solve for ...

But, I have an easier way. Solving for that equation can get messy. Instead, let us*hope*that its solutions are integers. Not necessarily this approach might work but let us try it, if it works then we can save a lot of work. If it does not we can try another way.

Note,

.

Now, so . It must be that . Are**factors**of . Since must be a square and positive. It means . Thus, the solutions are . Now take the square root to remove the square on to get: .

Now which of these pairs satisfies equation 2, i.e. .

We easily see that is the only solution.

Thus, .

Thus, .