Question

Find all zeros for the polynomial g(x) = x⁴

+ 10xt + 27x²+ 10x + 26 given x = i.
a. i and -i
b. 2i and -2i
c. 3i and -3i
d. No complex roots

Answer 1

The polynomial g(x) = x⁴+ 10xt + 27x²+ 10x + 26 given x = i does not have a zero when x = i.

Step-by-step explanation:

To find the zeros of the polynomial g(x) = x⁴+ 10xt + 27x²+ 10x + 26 given x = i, we need to substitute i into the polynomial and solve for when the polynomial equals zero.

Substituting i into the polynomial, we get: g(i) = i⁴ + 10i² - 27 + 10i + 26

Simplifying this expression, we have: g(i) = -11 + 10i

So, there is no zero for the polynomial g(x) when x = i.