We know that while finding the root of a quadratic equation ax2+bx+c=0 by quadratic formula x=−b±√b2−4ac2a,
if b2−4ac>0, then the roots are real and distinct
if b2−4ac=0, then the roots are real and equal and
if b2−4ac<0, then the roots are imaginary.
Here, the given quadratic equation 2n2+5n−1=0 is in the form ax2+bx+c=0 where a=2,b=5 and c=−1, therefore,
b2−4ac=(5)2−(4×2×−1)=25+8=33>0
Since b2−4ac>0
Hence the roots are real and distinct.