Mathematico | Mathematico

The line $y = m x$ is tangent to the parabola $y = x^{2} + 1$ .

Give the product of the possible values of $m$ .

Hint

The equation

x^{2} + 1 = m x

is required to have only one real solution. Use the discriminant.

Solution

The equation

\begin{aligned} x^{2} + 1 & = m x \\ x^{2} - m x + 1 & = 0 \end{aligned}

has only one solution.

Considering the discriminant

\begin{aligned} Δ & = 0 \\ m^{2} - 4 & = 0 \\ (m - 2) (m + 2) & = 0 \\ m \in {- 2, 2} \end{aligned}