Correct Answer - Option 4 : 1440
Concept:
If α and β are the roots of equation , ax2 + bx + c =0
Sum of roots (α + β) = \(\rm \frac{-b}{a}\)
Product of roots (αβ) = \(\rm \frac{c}{a}\)
(x + y)3 = x3 + y3 + 3xy (x + y)
Calculation:
x2 - 12x + 8 = 0
α & β are the roots of the equation .
⇒ α + β = 12 and αβ = 8
Now,(α + β)3 = α3 + β3 + 3αβ ( α + β )
⇒ (12)3 = α3 + β3 + 3× 8 × (12)
⇒ α3 + β3 = 1440 .
The correct option is 4.
