Question

For what values of a, the quadratic equation 9x² – 3ax + 1 = 0 has real and equal roots?

Answer 1

Let 9x² – 3ax + 1 = 0 be a quadratic equation.

It is given that, it has real and equal roots.

$$\begin{gathered} \Rightarrow \mathrm{Discriminant}=0 \\ \Rightarrow b^2-4ac=0 \\ \Rightarrow {\left(-3a\right)}^2-4\left(9\right)\left(1\right)=0 \\ \Rightarrow 9a^2=36 \\ \Rightarrow a^2=4 \\ \Rightarrow a=\pm 2 \end{gathered}$$

Hence, the values of a are –2 and 2.