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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Suppose you know that 1/3 and -2 are zeros of 3x^4-x^3-21x^2-11x+6
Find all the zeros!
Hint: 1/3 and -2 are zero of (3x-1)(x+2).
You need the Remainder Theorem.
How's your Synthetic Division? Long division?
not really good:(
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.
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).
Hello,
I'd do it this way :Quote:
Originally Posted by gumi
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...