ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: kaanonball on February 04, 2009, 07:40:25 pm

Title: Polynomial question
Post by: kaanonball on February 04, 2009, 07:40:25 pm: The expressions $px^4-5x +q$ and $x^4- 2x^3- px^2- qx - 8$ have a common factor x − 2. Find the values of p and q.

so does that mean that if they are divided by x - 2 they will equal 0?

any help would be appreciated
Title: Re: Polynomial question
Post by: dekoyl on February 04, 2009, 07:48:12 pm: Yes you're right.
Let $f(x) = px^4-5x +q$ and $g(x) = x^4- 2x^3- px^2- qx - 8$

$f(2) = 16p + q - 10 = 0$

$g(2) = -4p - 2q - 8 = 0$

Solve simultaneously.

Edit: But you're doing methods CAS. So you may be able to use matrices or something.

Answer (I think): p = 1, q = -6
Title: Re: Polynomial question
Post by: kaanonball on February 04, 2009, 07:59:00 pm: oks thanks!