For what values of a, the quadratic equation
Question:

For what values of $a$, the quadratic equation $9 x^{2}-3 a x+1=0$ has real and equal roots?

Solution:

Let $9 x^{2}-3 a x+1=0$ be a quadratic equation.

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

$\Rightarrow$ Discriminant $=0$

$\Rightarrow b^{2}-4 a c=0$

$\Rightarrow(-3 a)^{2}-4(9)(1)=0$

$\Rightarrow 9 a^{2}=36$

$\Rightarrow a^{2}=4$

$\Rightarrow a=\pm 2$

Hence, the values of a are –2 and 2.