Correct Answer - Option 2 : 165
Concept:
Consider a quadratic equation: ax2 + bx + c = 0.
Let, α and β are the roots.
- Sum of roots = α + β = -b/a
- Product of the roots = α × β = c/a
Calculation:
Given:
Quadratic equation is 5x2 - 8x – α = 0 and roots are -5 and 2β
Now, sum of roots = -5 + 2β = -(-8)/5 = 8/5
⇒ 2β = 8/5 + 5 = 33/5
Now, Product of the roots = (-5)(2β) = -α/5
⇒ -5(33/5) = -α/5
⇒ α = 33 × 5 = 165
Hence, option (2) is correct.