State whether the quadratic equation $2 x^{2}+x-1=0$ has two distinct real roots. Justify your answer.
(A) The given quadratic equation is $2 x^{2}+x-1=0$.
Comparing this with the standard form $a x^{2}+b x+c=0$,we get $a=2$,$b=1$,and $c=-1$.
The discriminant $D$ is given by the formula $D = b^{2}-4 a c$.
Substituting the values,we get $D = (1)^{2}-4(2)(-1) = 1+8 = 9$.
Since $D > 0$,the quadratic equation has two distinct real roots.
Comparing this with the standard form $a x^{2}+b x+c=0$,we get $a=2$,$b=1$,and $c=-1$.
The discriminant $D$ is given by the formula $D = b^{2}-4 a c$.
Substituting the values,we get $D = (1)^{2}-4(2)(-1) = 1+8 = 9$.
Since $D > 0$,the quadratic equation has two distinct real roots.
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