Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

Condition of divisibility

If

divides

then what condition must there be?

Using the factor theorem I get

, which is what the answer says.

But doesn't there have to be ANOTHER restriction for this to be true?

i.e.

So then doesn't

OR is this second restriction Not necessary???

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Condition of divisibility

What is c? If c can be complex as well as real, then there is no need for any condition on a and b. The condition

is only for required for c to be real.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Condition of divisibility

We haven't learnt complex numbers yet so I assume c is real.

Thanks Jane

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Condition of divisibility

Given that a quadratic has a single real root, it must be that there are two real roots, counting a repeated root as two roots.  That is the equivalent of your statement.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."