polymonials question (1 Viewer)

[reggina_calcio]

Im a yr 11 student going into yr 12 and we've just started on Polynomials - our first 3u topic. It was all smooth sailing untill we came up to roots and their realtionships with coefficients. This stuff has got the calss stumped.

Can someone please show me how to do this question..?:

Find two values of m such that the roots of the equation x^3 + 2x^2 +mx -16 = 0 are alpha, beta and alpha beta.

I remeber in year 9/10 everyone freaking out about a surds test....so i hope this is kind of liek then...and in a few months i';; be laughing at this sort of question...

Hopefully

Thanks in advance.

 

[withoutaface]

a^2b^2=16
ab=+/-4

then sub in x=4 and x=-4 and solve each for m

 

[velox]

Remember 16 is the product of the roots. So as the roots are alpha, beta and alpha beta. Multiply them and you get (a^2)(b^2) which is equal to 16. Then (ab) = +/- 4. M = -20 and M = -12.

 

[reggina_calcio]

Woa, thanks for the quick reply. Im kind of getting the hang of it now. I just need to do more drill.

Thanks again.

 

[velox]

Just learn your product of roots two at a time, 3 at a time etc stuff and with a bit of practice this topic should be a breeze.

 

[nit]

Wow...it's weird to read these threads after exams. That's all I've got to say

Maybe not...yeh, sums and products of roots are important. Just handle everything systematically in terms of the factor theorem/long division and sums and products of roots basically. There isn't a terribly wide scope of polynomial q's in 3u that you will be asked I don't think, and the arithmetic should be pretty sweet.