Question

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

Answer 1

Let x² + 4x + k = 0 be a quadratic equation.

It is given that, it has real roots.

$$\begin{gathered} \Rightarrow \mathrm{Discriminant}\ge 0 \\ \Rightarrow b^2-4ac\ge 0 \\ \Rightarrow {\left(4\right)}^2-4\left(1\right)\left(k\right)\ge 0 \\ \Rightarrow 16-4k\ge 0 \\ \Rightarrow 16\ge 4k \\ \Rightarrow 4k\le 16 \\ \Rightarrow k\le 4 \end{gathered}$$

Hence, the values of k must be less than or equal to 4.