2. The sum of the roots of (x2 + x -2)(x2 + x - 3) = 12 is:
1) -2 2) -1 3) 1 4) 2
Ans: (1)
Sol: (x2 + x)2 - 5 (x2 + x) - 6 = 0
x4 + 2x3 - 4x2 - 5x - 6 = 0
... S1 = -2
6. If (1 + i) is a root of the equation x2 - x - i + 1 = 0, then the other root is:
1) 1 - i 2) 1 3) -i 4) i
Ans: (3)
Sol: S1 = sum of roots = 1
one root is (1 + i)
... the other root is (-i)
7. If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5, then
1) -6 < a < 6 2) -3 < a < 3 3) -4 < a < 4 4) -5 < a < 5
Ans: (2)
Sol: (α - β) < √5
(α - β)2< 5
(α + β)2 - 4αβ < 5
(-a)2- 4(1) < 5
a2< 9 
-3 < a < 3
8. If α, β are the roots of x2 + x + 1 = 0, then α22, β19 will be the roots of the equation
1) x2 + x + 1 = 0 2) x2 + x - 1 = 0 3) x2 - x + 1 = 0 4) x2 - x - 1 = 0
Ans: (1)
