Root-Coefficent Relationships(6)

1. Sum of roots = a + 2a = 3a = 12
a = 4
The two roots are 4 and 8.
Product of roots = 4*8 = 32 = k
Hence a = 4 and k = 32
2. Product of roots = 2a^2 = 12
a^2 = 6
a = sqrt 6 or -sqrt 6
When a = sqrt 6, sum of roots = 3a = -k
3sqrt 6 = -k
k = -3sqrt 6
When a = -sqrt 6, sum of roots = -3sqrt 6 = -k
k = 3 sqrt 6