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Question: If a, b, g are roots of x<sup>3</sup> – mx<sup>2</sup> + 3x – m = 0, then general value of tan<sup>...

If a, b, g are roots of x3 – mx2 + 3x – m = 0, then general

value of tan–1a + tan–1b + tan–1g is-

A

Depends on m

B

Depends on p

C

np

D

(2n + 1) π2\frac { \pi } { 2 }

Answer

np

Explanation

Solution

Q Sum of roots = tan–1 a + tan–1b + tan–1 g = m

Product of roots = tan–1 a tan–1b tan–l g = m

Using formulae of tan (A + B + C)

tan (tan–1 a + tan–1 b + tan–1 g )

= tan

= tan ((m−m)1−∑tan⁡−1αtan⁡−1β)\left( \frac { ( \mathrm { m } - \mathrm { m } ) } { 1 - \sum \tan ^ { - 1 } \alpha \tan ^ { - 1 } \beta } \right) = 0

Ž tan–1a + tan–1 b + tan–1 g) = np