Question

If difference of roots of equation x2)-7x+2k=0, is 1 then find k

Answer 1

let the roots be p and q
the equation is x²-7x+2k=0
p-q=1 .....(given)
p=1+q........(1)
as we know
sum of roots =-b/a
p+q=-(-7)/1
p+q=7
1+q+q=7. ( from equation 1)
1+2q=7
2q=7-1
2q=6
q=3 put value of q in equation (1)
p=1+q
p=1+3
p=4
product of roots = c/a
p*q=c/a
(4)(3)=2k
12=2k
k=6 ....answer