- #1
an_mui
- 47
- 0
If m, n, and 1 are non-zero roots of the equation [tex]x^3 - mx^2 + nx - 1 = 0[/tex], then find the sum of the roots
This is what I did..
m, n, 1 are the roots. m and n not equal to 0
[tex]x^3 - mx^2 + nx - 1 = 0[/tex]
f(m) = 0 --> m^3 - m^3 + mn - 1
1 = mn (1)
f(1) = 1 - m + n - 1 = 0
... m = n (2)
Sub (2) --> (1)
[tex]m^2 = 1 [/tex]
[tex]m = +/- 1
since m and n are equal... the roots must be either 1, 1, 1 or -1, -1, 1. The answer on the sheet says the answer is -1. So my question is, how do we determine which roots are the answers. Thanks
This is what I did..
m, n, 1 are the roots. m and n not equal to 0
[tex]x^3 - mx^2 + nx - 1 = 0[/tex]
f(m) = 0 --> m^3 - m^3 + mn - 1
1 = mn (1)
f(1) = 1 - m + n - 1 = 0
... m = n (2)
Sub (2) --> (1)
[tex]m^2 = 1 [/tex]
[tex]m = +/- 1
since m and n are equal... the roots must be either 1, 1, 1 or -1, -1, 1. The answer on the sheet says the answer is -1. So my question is, how do we determine which roots are the answers. Thanks