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.
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