Finding all possible rational zeros.

Algebra
Tutor: None Selected Time limit: 1 Day

Use the rational zeros theorem to list all possible rational zeros of the following.

g(x)= 10x^3 + 3x^2 - 8x + 4

Be sure that no value in your list appears more than once.

Oct 17th, 2015

Hello!

By the theorem all possible rational zeroes have a form (factor of free term)/(factor of leading coefficient).

The factors of the free term (4) are +-1, +-2 and +-4. The factors of the leading coefficient (10) are +-1, +-2, +-5, +-10.

So the list (maybe with repetitions) is

+-1/1, +-1/2, +-1/5, +-1/10,
+-2/1, +-2/2, +-2/5, +-2/10,
+-4/1, +-4/2, +-4/5, +-4/10.

Let's simplify where possible:

+-1, +-1/2, +-1/5, +-1/10,
+-2, +-1, +-2/5, +-1/5,
+-4, +-2, +-4/5, +-2/5.

Now without repetitions the answer is:
+-1, +-2, +-4, +-1/2, +- 1/5, +-2/5, +-4/5, +-1/10.
(16 options)


Please ask if something is unclear.
Oct 17th, 2015

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