Sec3: Sum and Product of Roots (AMaths)

A = alpha

B = beta

Question:

Given that p is a constant and the quadratic equation x² - 4px + 15p = 0 has roots A and B, find the values of A and B and p for which

a) A : B = 3 : 5

b) A = B + 18

PS: I got the answers but i need the workings to understand on how to do questions like this.

a) A = 6, B = 10, p = 4

b) A = 3, B = -15, p = -3 OR A = 22.5, B = 4.5, p = 13.5

Hi,

Sum of roots A + B = 4p -- (1)

Product of roots AB = 15p -- (2)

In (a), we are given that A : B = 3 : 5, so A = 3/5 B.

From (1), 8/5 B = 4p, so B = 5/2 p and A = 4p - 5/2 p = 3/2 p.

From (2), (3/2 p)(5/2 p) = 15p, from which p can be solved.

Try part (b), thanks!

Cheers,
Wen Shih

Thanks a lot Wen Shih.

Btw congrats on being new mod ;P

Hi,

Thanks :)

Cheers,
Wen Shih