The other three zeros of f(x) = -2i is a zero of [tex]f(x) = x^4 - 45x^2 - 196[/tex] are 2i, 7, and -7.
We have to determine, using the given zero, find all other zeros of f(x). -2i is a zero of [tex]f(x) = x^4 - 45x^2 - 196[/tex].
According to the question,
The given function is [tex]f(x) = x^4 - 45x^2 - 196[/tex]
Given Zero of the function [tex]f(x) = x^4 - 45x^2 - 196[/tex] is -2i
The zeros of a function refer to those values that make f(x) = 0
f(x) has one zero is -2i, that means the second zero must be 2i,
because complex solutions happen in conjugate pairs.
The 2 zeros left can be found by evaluating the function with divisors of the constant term,
Which are by testing each one of these divisors 1, 2, 3, 4, 5, 6, 7...
[tex]f(7) = 74 - 45(72) - 196\\\\= 2401 - 2205 - 196 = 0[/tex]
The other zeroes numbers 7 and -7 are zeros of the function.
Complex roots. Other zeros of f(x) - 2i is a zero of [tex]f(x) = x^4 - 45x^2 - 196[/tex] are 2i, 7, and -7. The solution appears in pairs as if a is satisfied by the equation then -a also satisfies.
Therefore, the function has only pair exponents, which means positive and negative give the same result as you observed above.
Therefore, the other three zeros of the given function are 2i, 7, and -7.
To know more about Complex roots click the link given below.
https://brainly.com/question/12935822
