Question

If the equation mx² + 2x + m = 0 is satisfied by only one real value of x, then the values of m are ______ and ______.

Answer 1

Let mx² + 2x + m = 0 be a quadratic equation.

Since, the equation is satisfied by only one real value of x
Therefore, the roots are real and equal.

$$\begin{gathered} \Rightarrow \mathrm{Discriminant}=0 \\ \Rightarrow b^2-4ac=0 \\ \Rightarrow {\left(2\right)}^2-4\left(m\right)\left(m\right)=0 \\ \Rightarrow 4-4m^2=0 \\ \Rightarrow 4m^2=4 \\ \Rightarrow m^2=1 \\ \Rightarrow m=\pm 1 \end{gathered}$$

Hence, the values of m are 1 and −1.