Question

What is the value of k?

Find the value of k if `x^3 - 3x + a = 0` has three real distinct roots

Answer 1

If `a = k`, then `-2 < k < 2`

Explanation:

Given: `x^3 - 3x + a = 0`

The top graph is `x^3 - 3x + 2 = 0 " "=>" "` only has two real roots.

The bottom graph is `x^3 - 3x + 2 = 0 " "=>" "` only has two real roots.

This means if `a = k`, then `-2 < k < 2`
graph{(y - x^3 + 3x - 2) (y - x^3 +3x + 2)= 0 [-10, 10, -5, 5]}

Graph when `a = 1`:
graph{x^3 - 3x + 1 [-10, 10, -5, 5]}