Find the value of #c# for which the roots of #2x^2-21x+c=0# are in the ratio #1:2#?

1 Answer
Jun 27, 2017

Answer:

#c=49#

Explanation:

When we have two roots of #ax^2+bx+c=0#, then

sum of roots is #-b/a# and product of roots ic #c/a#.

As roots of #2x^2-21x+c=0# are in the ratio #1:2#, let the roots be #alpha# and #2alpha#.

Then #alpha+2alpha=21/2# i.e. #3alpha=21/2# or #alpha=7/2#.

and hence as #c/2# is product of roots, we have

#c/2=7/2xx2xx7/2=49/2#

or #c=49#