Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between (A) -1, -3 (B) 1, -3 (C) -1, 2 (D) -1, 3 (E) 1, 3 [spoiler]Made up[/spoiler]

sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between (A) -1, -3 (B) 1, -3 (C) -1, 2 (D) -1, 3 (E) 1, 3 Nice idea, sanju09! I will give my shot, ok? Answer: D Let the expression given be equal to m, where m is a fixed real number. It is easy to come to the following 2o degree equation in the (real) variable x: x^2 - x(1+m)+(1+m) = 0 Calculating the discriminant and imposing it NEGATIVE, we will get m^2 - 2m - 3 < 0, then we have -1 < m < 3. Interpretation: for values of m between -1 and 3, there are no real numbers x such that the expression is equal to m. That´s what you had in mind? Best Regards, Fábio.

sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between (A) -1, -3 (B) 1, -3 (C) -1, 2 (D) -1, 3 (E) 1, 3 [spoiler]Made up[/spoiler] IMO D. Just tried some value by taking x=0,1,-1,-1/2

fskilnik wrote:sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between (A) -1, -3 (B) 1, -3 (C) -1, 2 (D) -1, 3 (E) 1, 3 Nice idea, sanju09! I will give my shot, ok? Answer: D Let the expression given be equal to m, where m is a fixed real number. It is easy to come to the following 2o degree equation in the (real) variable x: x^2 - x(1+m)+(1+m) = 0 Calculating the discriminant and imposing it NEGATIVE, we will get m^2 - 2m - 3 < 0, then we have -1 < m < 3. Interpretation: for values of m between -1 and 3, there are no real numbers x such that the expression is equal to m. That´s what you had in mind? Best Regards, Fábio. hmmm...so you read minds too!! Well, you certainly deserve an on records 'THANKS' from me. Nice job, sir