Question

Family of lines x(a + b) + y = 1 where a and b are roots of the equation x3 – 3x2 + x + 1 = 0 and [a + b] = 1 (where [.] denotes the greatest integer function) such that it intercepts a triangle of area A with coordinate axes then Amax is-

• A. 1
• B. ½
• C. 2
• D. ¼

Answer 1

Answer: (B)

½

Answer 2

a + b + c = 3

a + b = 3 – c

[a + b] = [3 – c] = 1

1 < c £ 2

Area A = $\frac { 1 } { 2 }$ $\left( \frac { 1 } { 3 - c } \right)$ Ž $\frac { \mathrm { dA } } { \mathrm { dc } } = + \frac { 1 } { 2 ( 3 - \mathrm { c } ) ^ { 2 } }$ > 0 Ž A is increasing function

Amax = $\frac { 1 } { 2 }$ $\frac { 1 } { 2 }$ sq. units