Solve:
x^4-10x^3+42x^2-82x+65=0 the product of two of the roots of this equation is 13. The answers are complex numbers.
Thanks for helping me
Hello, Anand Parikh!
I approached it like CaptainBlack and got very lucky . . .Solve: .
The product of two of the roots of this equation is 13.
The roots are complex numbers.
Since the product of two roots is 13,
. . I guessed that the roots were: .
If the roots are: .
. . then: . .are factors of
Hence: . .is a factor of
. . But does not divide
If the roots are: .
. . then: . .are factors of
Hence: . .is a factor of
. . And we have: .