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

Given:

To do:

We have to state whether the given quadratic equations have two distinct real roots.

Solution:

$2 x^{2}+x-1=0$

Comparing with $a x^{2}+b x+c=0$, we get,

$a=2, b=1$ and $c=-1$

Discriminant $D=b^{2}-4 a c$

$=(1)^{2}-4(2)(-1)$

$=1+8$

$=9>0$

$D>0$

Hence, the equation $2 x^{2}+x-1=0$ has two distinct real roots.

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Updated on: 10-Oct-2022

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