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The quadratic equation

x^{2} + k x + 5 = 0

has at least one solution.

Find the range of possible values of $k .$

Use the table below to find your answer based on your solution set.

Give your answer to the nearest integer.

Hint

Consider the discriminant.

Hint

b^{2} - 4 a c \geq 0

Solution

Since the equation has real roots (meaning at least one solution), we know the discriminant satisfies

\begin{aligned} b^{2} - 4 a c & \geq 0 \\ k^{2} - 4 (1) (5) & \geq 0 \\ k^{2} - 20 & \geq 0 \end{aligned}

We draw a sketch

parabola

From the sketch, we see that the solution is

k \leq - 2 \sqrt{5} or k \geq 2 \sqrt{5}