State whether the following quadratic equations have two distinct real roots. Justify your answer.
$ 3 x^{2}-4 x+1=0 $
Given:
\( 3 x^{2}-4 x+1=0 \)
To do:
We have to state whether the given quadratic equations have two distinct real roots.
Solution:
$3 x^{2}-4 x+1=0$
Comparing with $a x^{2}+b x+c=0$, we get,
$a =3, b=-4$ and $c=1$
Discriminant $D=b^{2}-4 a c$
$=(-4)^{2}-4(3)(1)$
$=16-12$
$=4>0$
$D>0$
Hence, the equation $3x^{2}-4 x+1=0$ has two distinct real roots.
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