Sec3 AMaths - Polynomials

Only-Way-4-Destiny! SG

Hi all, I need some help on this question.

Given that 2x² + 3px - 2q and x² + q have a common factor x - a, where p, q and a are non-zero constants, show that 9p² + 16q = 0.

Thanks.

dkcx SG

Replace x by a in both equations since (x-a) means x=a.

After that, from the 2nd equation, you can get a in terms of q, sub this a value into the 1st equation, do some manipulation and you will get the answer.

wee_ws SG

Hi,

Let f(x) = 2x² + 3px - 2q and g(x) = x² + q.

Then f(a) = 0 and g(a) = 0, by factor theorem.

So 2a² + 3pa - 2q = 0 -- (1)

and a² + q = 0 -- (2).

From (2), a² = -q, which we substitute into (1) to obtain:

-2q + 3pa - 2q = 0

=> 3pa = 4q

=> a = 4q/3p (remember that p is non-zero, and q is non-zero)

Substitute a into (2), we obtain:

(4q/3p)² = -q

=> 16q² = -9p²q

=> q(16q + 9p²) = 0, but q is non-zero, so ...

Thanks!

Cheers,
Wen Shih

Only-Way-4-Destiny! SG

Thanks!

SBS n SMRT SG

thanks, i also blur of this qns