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Question

If p,q,r are in A.P. and are positive, the roots of the quadratic equation px2+qx+r=0 are all real for 
  1. All p and r
  2. No p and r


Solution

The correct option is B
p,q,r are positive and are in A.P.
q=p+r2                   .....(i)
The roots of px2+qx+r=0 are real
q24pr[p+r2]24pr                          [using(i)]
p2+r214pr0     
(rp)214(rp)+10                 (p>0 and p0)
(rp7)2480(rp7)2(43)20
rp743.

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