Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If p, q, r are positive and are in A.P., the roots of quadratic equation px 2 + qx + r = 0 are all real for:
A
≥ 4 
B
≥ 4 
C
All p and r
D
No p and r
Text Solution
Verified by ExpertsThe correct answer is:
B
Roots are real, so D ≥ 0 p, q, r are in A.P.
q 2 ≥ 4pr So, q = 
⇒ 
≥ 4pr
⇒ p 2 + r 2 + 2pr ≥ 16 pr
⇒ p 2 + r 2 –14 pr ≥ 0
⇒ 
+ 
(14) + 1 ≥ 0
⇒ 
– 
+ 1 ≥ 0
= 
= 7 ± 4 
⇒ 
≤ 7 + 4 
, 
∈ 7 – 4 
⇒ 
≥ 4 
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