Question

If the root of x² + px + 12 = 0 are in the ratio 1:3 then what is the value of p ?

Answer 1

so let's take one root as y and other root becomes 3y as roots are in the ratio of 3:1 hence on putting x=y
${y}^{2 } + py + 12 = 0$
as well as
$9 {y}^{2} + 3py + 12 = 0$
hence on multiplying first equation by 3 we get 3y2+3py+36=0 hence 6y^2=24 so y=2 (or)-2 thus on keeping x=2 we get p=-8 and p=8