Question

Using the given zero, find one other zero of f(x). i is a zero of f(x).= x4 - 2x3 + 38x2 - 2x + 37.

Answer 1

If i is a zero of the polynomial, then the factor is (x - i). Because of the conjugate rule, it is understood that one other root of the polynomial HAS to be (x + i). So that's one other root. The other 2 roots are (1 + 6i) and (1 - 6i).

Answer 2

-i

Explanation:

Since the given function does not has any imaginary number.

And "i" is the imaginary number.So, other factor must be "-i" by conjugate rule.

Thus, One other factor is "-i".

For finding the other factors we will follow following steps:

The product of first and second factor is:

(x - i)(x + i) = x² - i² = x + 1

Now by dividing the given function f(x) = x⁴ - 2x³ + 38x² - 2x + 37 by (x + 1)

We get quadratic function. Then by Sidharyacharya Formula we will find other two factors.