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Roots of Polynomial Equations Watch

1. The equation has roots and . Find the equations which have the following roots.

,

I've tried letting the roots equal u. Rearrange for and and substitute them into the equation. But it hasn't worked, any ideas how to do this?

On this one again, I've let roots equal u. Then by using simultaneous equation I eliminated and substituted my into the quadratic. Again I get the wrong. Is this method not suitable for this kind of question?
2. You can do it the way you said (but it is not the most efficient way).

Rearrange to make the subject and square.

It is easier to use the identity

You can use a u substitution for the second one too.

You know so and
3. (Original post by Mr M)
You can do it the way you said (but it is not the most efficient way).

Rearrange to make the subject and square.

It is easier to use the identity

You can use a u substitution for the second one too.

You know so and
Thank you. For the first part isn't the answer just squared as it wanted the equation or is this why I'm not getting the same answer as the textbook?

And for the second part, I like your method. I'm just wondering why my original method didn't work.

can be rearranged as
and
can be rearranged as

I can substitute 2nd equation into 1st to get

And this value for is different to yours, so I must have gone wrong with my method some how?
4. (Original post by Freerider101)
Thank you. For the first part isn't the answer just squared as it wanted the equation or is this why I'm not getting the same answer as the textbook?

And for the second part, I like your method. I'm just wondering why my original method didn't work.

can be rearranged as
and
can be rearranged as

I can substitute 2nd equation into 1st to get

And this value for is different to yours, so I must have gone wrong with my method some how?
On the first thing you need to make the bit the subject so that it becomes positive when you square both sides.

On your second point, you are making the incorrect assumption that the roots of the new equation are equal (you have set them both equal to u).

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Updated: December 5, 2010
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