If the difference of the roots of #2x^2-6x+c=0# is 5, what are the roots? What is the value of c?

1 Answer
Jan 30, 2018

#c=-8#

Explanation:

In an equation #ax^2+bx+c=9#, sum of roots is #-b/a# and product of roots is #c/a#.

Let #alpha# and #beta# be the roots of #2x^2-6x+c=0#,

then #alpha+beta=6/2=3# and #alphabeta=c/2#

Now as #(alpha+beta)^2-4alphabeta=(alpha-beta)^2#,

we have #3^2-4*c/2=5^2#

or #9-2c=25# ir #2c=9-25=-16# i.e. #c=-8#