Correct Answer - Option 3 : 1.2 and -1.4
Given
Equation = x3 - 0.6x2 - 1.84x + 1.344 = 0
One root = 0.8
Concept
If α, β and γ are roots of equation ax³ + bx² + cx + d = 0, then
α + β + γ = -b/a
αβ + βγ + γα = c/a
αβγ = - d/a
calculation
Let, α = 0.8
Hence, 0.8 + β + γ = 0.6
⇒ β + γ = - 0.2 ---- (1)
By putting values of the other two roots we can find the answer.
From option 1, β + γ = 1.1 + (-1.4) = -0.3 (Not satisfied)
From option 2, β + γ = - 1.2 - 1.4 = -2.6 (Not satisfied)
From option 1, β + γ = 1.2 -1.4 = -0.2 (satisfied)
From option 1, β + γ = -1.1 - 1.4 = -2.5 (Not satisfied)
Hence, option 3 is the correct answer.