Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Set of real values of 
if the equation 
has at least one root in 
is
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
D
D ≥ 0
(k–1) 2 – 4k 2 ≥ 0 ⇒ (k + 1) (3k – 1) ≤ 0
Case- I Exactly one in (1,2)
f(1) f(2) < 0 ⇒ (1– k+1+1) (4–2k+2+k 2 )<0
⇒ (3 – k) (k 2 – 2k + 6) < 0
⇒ 3 – k < 0 ⇒ k > 3
if one roots is – 1 then k = 3
– 1 × k = 9 ⇒ k = – 9 ⇒ k 
3
if one root is 2 then k 2 – 2k + 6 = 0 not possible
⇒ 
Case-II If both roots lie in (1,2)
f(1) > 0 & f(2) > 0
3 – k > 0 ⇒ k < 3 & k 2 – 2k + 6 > 0
⇒ 
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