Posted by ladybug on Sunday, October 14, 2012 at 12:08am.
use the given zero to find the remaining zeros of the function.
h(x)=x^412x^3+36x^2+68x525
zero:43i

precal  Reiny, Sunday, October 14, 2012 at 1:01am
complex zeros always come in conjugate pairs
so if 43i is a root, so is 4+3i
so (x  4 3i)(x  4 + 3i) will be a factor
= x^2  4x + 3ix  4x + 16  12i  3ix + 12i  9i^2)
= x^2  8x + 25
Using long algebraic division
(x^4  12x^3 + 36x^2 + 68x  525) / (x^2  8x + 25)
= x^2  4x  21
so for x^2  4x  21 = 0
(x7)(x+3) = 0
x = 7 or x = 3
roots are :
3 , 7 , 4+3i , 43i
=
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