Suppose you know that 1/3 and -2 are zeros of 3x^4-x^3-21x^2-11x+6

Find all the zeros!

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- May 10th 2008, 05:10 PMgumifind the zeros
Suppose you know that 1/3 and -2 are zeros of 3x^4-x^3-21x^2-11x+6

Find all the zeros! - May 10th 2008, 05:28 PMTKHunny
Hint: 1/3 and -2 are zero of (3x-1)(x+2).

You need the Remainder Theorem.

How's your Synthetic Division? Long division? - May 10th 2008, 05:31 PMgumi
not really good:(

- May 10th 2008, 05:38 PMTKHunny
It's time to practice.

Every time you find a zero, use it to deflate the polynomial to one degree lower. Eventually, you'll get it down to quadratic and the last two are easy. - May 10th 2008, 06:03 PMsleepingcat
You could also use Vieta's Formulas and get the system

and solve it simultaneously for the other roots. You should get the same quadratic (I'm bad at synthetic division too). - May 11th 2008, 03:16 AMMoo
Hello,

I'd do it this way :

and are zeros of

Hence

where P is a polynomial of degree 2.

We can rewrite this way :

, but we don't care.

Since the first term is , a=1 because we would have 3x*x*ax˛ as the dominating term.

Hence

Let's study the constant term :

-1*2*c=6

->

Thus

Now, you can develop...