Question

If one root of the equation 5x² + 13x + k = 0 is the reciprocal of the other root then find the value of k.

Answer 1

Given: 5x² + 13x + k = 0 and one root is the reciprocal of the other.

Step-wise calculation:

1. Let the roots be α and β with `β = 1/α`, so αβ = 1 (α ≠ 0).

2. For ax² + bx + c = 0, product of roots = `c/a`.

Here product = `k/5`.

3. Set `k/5 = 1`

⇒ k = 5