Problema Solution
find the condition that one root of ax^2 +bx +c =0 may be n timesthe other
Answer provided by our tutors
let the 2 roots be x and 10x
using the Vieta's formulas we have
x + 10x = - b/a
x*10x = c/a
that is the conditions are
from 11x = -b/a we get x = -b/(11a) and plug into 10x^2 = c/a
10(-b/(11a))^2 = c/a
10b^2/(121a^2) = c/a multiply both sides by 121a^2
10b^2 = 121ca is the condition.