Question

For what value of k, the roots of the equation x² + 4x + k = 0 are real?

Answer 1

The given equation is `"x"^2 + 4"x" + "k" = 0`
For real roots, D ≥ 0
⇒ `"b"^2 – 4"ac" ≥ 0`
⇒ `4^2 – 4(1) ("k") ≥ 0`
⇒ 4 – k ≥ 0
⇒ `"k" ≤ 4`

For `"k" ≤ 4`, the given equation `"x"^2 + 4"x" + "k"` = 0 has real roots.