If eλ and e-A are the roots ofequation 3x2-(a+b)x + 2a-0, a b, λ e R

1.	If eλ and e-A are the roots ofequation 3x2-(a+b)x + 2a-0, a b, λ e R. λ#0 then least integralvalue of b is(A) 4Q.5(B) 5(C) 9(D) 10
Answer» given eⁿ and e-ⁿ are the roots so, according to the equation product of roots = 2a/3 => eⁿ * e-ⁿ = 2a/3 => 2a/3 = 1 => a = 3/2 sum of roots should be (a+b)/3 => (a+b)/3 = eⁿ +e-ⁿ=> (a+b) = 3( eⁿ +e-ⁿ) also, the minimum +ve value of a function x+1/x = 2 so , (a+b) = 3*2 => b = 6-a = 9/2 ... the least intergral value is > 9/2. = 5 option B

If eλ and e-A are the roots ofequation 3x2-(a+b)x + 2a-0, a b, λ e R. λ#0 then least integralvalue of b is(A) 4Q.5(B) 5(C) 9(D) 10

Answer»

given eⁿ and e-ⁿ are the roots

so, according to the equation product of roots = 2a/3 => eⁿ * e-ⁿ = 2a/3 => 2a/3 = 1 => a = 3/2

sum of roots should be (a+b)/3 => (a+b)/3 = eⁿ +e-ⁿ=> (a+b) = 3( eⁿ +e-ⁿ)

also, the minimum +ve value of a function x+1/x = 2

so , (a+b) = 3*2 => b = 6-a = 9/2 ... the least intergral value is > 9/2. = 5

option B