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