Hey guys

Solve the equation given that the sum of two of its roots is zero.

I have no idea how to solve this. I have never dealt with a quartic before.

Please, any help?

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- Jan 22nd 2010, 12:24 PMSunyataProduct + Sum of the Roots
Hey guys

Solve the equation given that the sum of two of its roots is zero.

I have no idea how to solve this. I have never dealt with a quartic before.

Please, any help? - Jan 22nd 2010, 01:27 PMDinkydoe
I admit this is not an easy problem.

Let

Suppose are roots such that . This means .

Thus we can write .

If we let .

we have

And since

And since .

Thus we found

Now you can find the roots of the 2 quadratic factors yourself. - Jan 22nd 2010, 04:44 PMSoroban
Hello, Sunyata!

Quote:

Solve the equation:

given that the sum of two of its roots is zero.

Then: .

Subtract [2] - [1]: .

. . and we have three roots: .

. . but is an exraneous root.

Hence, two of the factors are: .

Dividing , we get: .

The equation becomes: .

Therefore, the roots are: .