Question
Question: If a, b, c, d are four consecutive terms of an increasing AP, then the roots of the equation (x – a...
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
A
Real and distinct
B
Non real complex
C
Real and equal
D
Integers
Answer
Real and distinct
Explanation
Solution
f(x) = (x – a) (x – c) +2 (x – b) (x – d)
f(1) = 2 (a – b) (a – d) Ž +ve
f(2) = (b – a) (b – c) Ž – ve
f(3) = 2 (c – b) (c – d) Ž – ve
f(4) = (d – a) (d – c) Ž +ve
Hence, one root exists between a and b and other exists
between c & d. Hence real & distinct.