YLL討論網

if one root of 3x^2-4x+p=0 is three times the other root,find the value of p

push

Suppose the two roots are r and 3r.

Then we have
    3(x-r)(x-3r) = 0,

and thus
    3x² - 12rx + 9r² = 0 ...... (*)

Compare (*) to the original equation,
we obtain
    12r = 4 and 9r² = p.

Hence
r = 4/12 = 1/3 and p = 9(1/3)² = 1.