If a,b,c are in AP such that a+b+c=0,then roots of the equation px²+qx+b=0;(pq≠0) are

a.real and identical

b.real and distinct

c.imaginary

d.none of these

Hi Menka,

Now a,b,c are in AP. So 2b=a+c

a+b+c = 0, will give 3b=0 or b=0.

Hence the QE becomes, px^2 + qx = 0.

Hence one root is 0, and the other is -q/p.

Since pq is not zero, the value -q/p can never be 0.

Hence real and distinct roots. Option (B).

Hope it helps.

Best Regards,

Ashwin (IIT Madras).

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