State whether the following quadratic equations have two distinct real roots. Justify your answer.
$ 3 x^{2}-4 x+1=0 $

AcademicMathematicsNCERTClass 10

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.

raja
Updated on 10-Oct-2022 13:27:26

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