# polynomial roots

• Sep 1st 2009, 03:13 AM
deej813
polynomial roots
the polynomial x^3 - 4x^2 + 5x - 1 = 0 has 3 roots a,b and y
i. find the value of a + b + y
ii. find the value of aby
iii. find the equation of the polynomial with roots 2a, 2b and 2y

i got 4 for i and 1 for ii
are these right??
how do you do iii.?
• Sep 1st 2009, 03:53 AM
Opalg
Quote:

Originally Posted by deej813
the polynomial x^3 - 4x^2 + 5x - 1 = 0 has 3 roots a,b and y
i. find the value of a + b + y
ii. find the value of aby
iii. find the equation of the polynomial with roots 2a, 2b and 2y

i got 4 for i and 1 for ii
are these right?? Yes.
how do you do iii.?

If $x^3 - 4x^2 + 5x - 1 = 0$ has roots a, b and y then $(x/2)^3 - 4(x/2)^2 + 5(x/2) - 1 = 0$ has roots 2a, 2b and 2y.
• Sep 1st 2009, 04:25 AM
deej813
really?
how do you work that out?
do i simplify to
x^3/8 - 4x^2/4 + 5x/2 -1 = 0 ??
• Sep 1st 2009, 05:08 AM
ynj
Quote:

Originally Posted by deej813
really?
how do you work that out?
do i simplify to
x^3/8 - 4x^2/4 + 5x/2 -1 = 0 ??

since if $x=a$is a root for $f(x)$, then $2a$is a root for $f(\frac{x}{2})$
• Sep 1st 2009, 12:30 PM
deej813
oh ok i get it
thanks