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Question

Discuss the nature of roots of the given equation: 2n2+5n1=0

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Solution

We know that while finding the root of a quadratic equation ax2+bx+c=0 by quadratic formula x=b±b24ac2a,
if b24ac>0, then the roots are real and distinct
if b24ac=0, then the roots are real and equal and
if b24ac<0, then the roots are imaginary.

Here, the given quadratic equation 2n2+5n1=0 is in the form ax2+bx+c=0 where a=2,b=5 and c=1, therefore,
b24ac=(5)2(4×2×1)=25+8=33>0

Since b24ac>0

Hence the roots are real and distinct.

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