Question

If α, β be the zeros of the polynomial 2x² + 5x + k such that `α^2 + β^2 + αβ = 21/4` then k = ?

Options

• 3

• –3

• –2

• 2

Answer 1

2

Explanation:

For 2x² + 5x + k, sum of roots `α + β = -5/2` and product `αβ = k/2`.

α² + β² = (α + β)² – 2αβ 

= `(-5/2)^2 - 2(k/2)`

= `25/4 - k`

So, `α^2 + β^2 + αβ = (25/4 - k) + (k/2)`

= `25/4 - k/2` 

Set equal to `21/4`:

`25/4 - k/2 = 21/4` 

⇒ `1 - k/2 = 0` 

⇒ k = 2