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?

Answer 1

\[ 1/ab + 1/bc + 1/ac =(bc*ac+ab*ac+ab*bc)/(ab*bc*ac)\]
\[(ab*c^2+a^2*bc+ac*b^2)/(abc)^2\]
taking abc common
\[abc(c+a+b)/(abc)^2\]
(a+b+c)/abc

Answer 2

so it is sum of root divide by product of root

Answer 3

let Ax^3 + Bx^2 + Cx + D = 0,
a*b*c = -D/A
a+b+c = -B/A
so in your Q D=-11 and A=1 and B=-4
a*b*c= -(-11)/1 =11 a+b+c =-(-4)/1=4
(a+b+c)/abc =4/11

Answer 4

@wengzie2.0

Answer 5

woah..thanks..i'll read itfirst. thank you. :)

Answer 6

isn't the a,b,c are the roots of the equation, but in your solution you used it as the coefficient of the equation. im confused.

Answer 7

no they are A B C D different from root abc
in place A B C D you can use P Q R S

Answer 8

@wengzie2.0 got?????

Answer 9

not yet...

Answer 10

Px^3 + Qx^2 + Rx +S =0
now?????