Question

if α and β are the roots of the equation 2x² - x + 1 = 0 then what is the value of α³ + β³ = ?
1. -6/8
2. -5/8
3. 3/5
4. 5/3

Answer 1

Correct Answer - Option 2 : -5/8

Concept:

Product of roots = (-b/a), Sum of roots = (c/a)

(a³ + b³) = (a + b)³ - 3ab × (a + b)

Calculation:

From the equation a = 2, b = -1, c = 1

⇒ α × β = c/a = 1/2, α + β = (-b/a) = -(-1/2) = 1/2

⇒ α³ + β³ = (1/2)³ - 3 × (1/2) × (1/2) = (1/8 - 3/4) = -5/8

∴ The required result will be -5/8.