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
All p and r
No p and r
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 ⇒q2≥4pr⇒[p+r2]2≥4pr [using(i)] ⇒p2+r2−14pr≥0 ⇒(rp)2−14(rp)+1≥0(∵p>0 and p≠0) ⇒(rp−7)2−48≥0⇒(rp−7)2−(4√3)2≥0 ⇒∣∣rp−7∣∣≥4√3.