Correct Answer - Option 2 : 3
Concept:
If third order equation ax3 + bx2 + cx + d =0 has a root α, β and γ then;
\(α + β + γ = - \frac{b}{a}\)
\(α β + β γ + γ α = \frac{c}{a}\)
\(α β γ = - \frac{d}{a}\)
Calculation:
Given:
x3 - 12x2 + 39x - 28 = 0
Let roots of given equation is α – d, α, α + d
\(α - d + α + α + d = - \frac{{ - 12}}{1}\)
3 α = 12
α = 4
\(\left( {α - d} \right)\left( α \right)\left( {α + d} \right) = - \left( {\frac{{ - 28}}{1}} \right)\)
4 – d ⋅ 4 ⋅ 4 + d = 28
16 – d2 = 7
D2 = 16 - 7 = 9
D = 3
