Question

If α, β are the roots of the equation 2x² – 3x – 4 = 0, then what is the value of α² + β²?
1. 9/4
2. 25/4
3. 27/4
4. 31/4

Answer 1

Correct Answer - Option 2 : 25/4

Given:

Equation 2x2 – 3x – 4 = 0

Formula Used:

sum of roots = (-b/a), product of roots = c/a; where symbol have their usual meaning

Calculation:

⇒ α + β = 3/2    .....(i)

⇒ αβ = -2

On squaring equation (i), we have

⇒ (α + β)² = α2 + β² + 2αβ

⇒ 9/4 = α2 + β2 + 2 × (-2)

⇒ α2 + β2 = 25/4

∴ Required value = 25/4