Published by:
CGP EDU Academic Team
Published on: August 13, 2026
For real x, the function 
assume all real values provided
Text Solution
Verified by ExpertsThe correct answer is:
D
yx - cy = x 2 - (a + b)x + ab
x 2 - (a + b + y)x + (ab + cy) = 0
For real roots, D 
0
(a + b + y) 2 - 4 (ab + cy) 
0
(a + b) 2 + y 2 + 2 (a + b)y - 4ab - 4cy 
0
y 2 + 2(a + b - 2c)y + (a - b) 2 
0
which is true for all real values of y if
D 
0
4(a + b - 2c) 2 - 4(a - b) 2 
0
(a + b - 2c + a - b)(a + b - 2c - a + b) 
0
(2a - 2c) (2b - 2c) 
0
(a - c) (b - c) 
0
(c - a) (c - b) 
0
c must lie between a and b
i.e., a 
c 
b or b 
c 
a
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