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CGP EDU Academic Team
Published on: August 13, 2026
If a, b, c, d are four consecutive terms of an increasing AP, then the roots of the equation (x – a) (x – c) + 2 (x – b) (x – d) = 0 are
Text Solution
Verified by ExpertsThe correct answer is:
A
f(x) = (x – a) (x – c) +2 (x – b) (x – d)
f(a) = 2 (a – b) (a – d) ⇒ +ve
f(b) = (b – a) (b – c) ⇒ – ve
f(c) = 2 (c – b) (c – d) ⇒ – ve
f(d) = (d – a) (d – c) ⇒ +ve
Hence, one root exists between a and b and other exists between c & d. Hence real & distinct.
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