find the polynomial that satisfies the following conditions:
4th degree where i and 6i are the zeros
I can't figure it out I forget how to do it
when i , 6i are zeros of the polynomial then -i , -6i are the other zeros of the polynomial.
then the polynomial is
( x + i ) ( x - i ) ( x + 6i ) ( x - 6i )
=> ( x^2 + 1 ) ( x^2 + 36 )
=> x^4 + 37x^2 + 36
If i is a zero, so is -i.
Id 6i is a zero, so is -6i.
(x - i)(x + i)(x - 6i)(x + 6i) = 0
(x^2 + 1)(x^2 + 36) = 0
x^4 + 37x^2 + 36 = 0
f(x) = x^4 + 37x^2 + 36
69
Comments
when i , 6i are zeros of the polynomial then -i , -6i are the other zeros of the polynomial.
then the polynomial is
( x + i ) ( x - i ) ( x + 6i ) ( x - 6i )
=> ( x^2 + 1 ) ( x^2 + 36 )
=> x^4 + 37x^2 + 36
If i is a zero, so is -i.
Id 6i is a zero, so is -6i.
(x - i)(x + i)(x - 6i)(x + 6i) = 0
(x^2 + 1)(x^2 + 36) = 0
x^4 + 37x^2 + 36 = 0
f(x) = x^4 + 37x^2 + 36
69