Here is your answer
d) [tex]r2= -5-\sqrt{5}[/tex]
REASON:
Equation is-
[tex] 2{x}^{2}+8x+c=0 [/tex]
Here,
a= 2; b= 8 and c=c
Now,
[tex] r1+r2= -b/a [/tex]
[Relation used: sum of zeroes=
-coefficient of x/ coefficient of x^2]
So,
[tex] 1+\sqrt{5} + r2= -8/2 [/tex]
[tex] 1+\sqrt{5} + r2= -4 [/tex]
[tex] r2= -4-1-\sqrt{5} [/tex]
[tex] r2= -5-\sqrt{5} [/tex]
HOPE IT IS USEFUL