P(x) = x^3 - 4x^2 + 8x - 11 has roots a, b, c. What is the VALUE of the expression (1/ab) + (1/bc) + (1/ac)?

PLEASE HELP ME. Thank you. I've tried solving this, but I'm so confused. I thought the roots were (+-1,+-11) but there's always a remainder. How am I going to solve it?

Question

P(x) = x^3 - 4x^2 + 8x - 11 has roots a, b, c. What is the VALUE of the expression (1/ab) + (1/bc) + (1/ac)? 

PLEASE HELP ME. Thank you. I've tried solving this, but I'm so confused. I thought the roots were (+-1,+-11) but there's always a remainder. How am I going to solve it?

ranga · Answer

If P(x) has roots a, b and c it means P(x) = (x - a)(x - b)(x - c) 
x^3 - 4x^2 + 8x - 11 = (x - a)(x - b)(x - c) 
Expand the right and equate coefficients of like terms.
You will get 3 equations with 3 unknowns: a, b, and c.
You don't really have to solve for a, b, c
They want you to evaluate (1/ab) + (1/bc) + (1/ac)
which can be written as: (a + b + c)/abc
When you equate the coefficients you will already have one equation (a + b + c) = some constant and abc = another constant.  Substitute and you can evaluate what they want without really solving for a, b and c!