Question

If one root of the equation ax^2+bx+c=0 is three times the other ,then b^2:ac::

Answer 1

LET TWO ROOT OF EQUATION ARE d band 3d

then according to ques,

sum of root=>

d+3d=-b/a

solving this we get

4d=-b/a..........eqn 1

and product of root

3d^2=c/a..........eqn 2

putting value of d from eqn 1 into 2 we get

3b^2/16a=c

so 3b^2=16ac