Using the given zero, find all other zeros of f(x). -2i is a zero of f(x) = x⁴ - 45x² - 196

Solution:

The given function is f(x) = x⁴ - 45x² - 196

Given Zero of the function f(x) = x⁴ - 45x² - 196 is -2i

The zeros of a function refer to those values that make f(x) = 0

We know that given that 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....

We found that numbers 7 and -7 are zeros of the function.

f(7) = 7⁴ - 45(7²) - 196

= 2401 - 2205 - 196 = 0

Therefore, the function has only pair exponents, that 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.

Using the given zero, find all other zeros of f(x). - 2i is a zero of f(x) = x⁴ - 45x² - 196

Summary:

Complex roots.Other zeros of f(x) - 2i is a zero of f(x) = x⁴ - 45x² - 196 are 2i, 7 and -7. The solution appears in pairs as if a is satisfied by the equation then -a also satisfies.