Question

Find the polynomial equation of lowest degree, with real coefficients and leading coefficient 1 1 that has the given roots.

Answer 1

Answer:

x^4 + 2x^3 + 3x^2 + 2x + 2 = 0

Step-by-step explanation:

The computation of the polynomial equation of the lowest degree is shown below

As we know that the complex roots would always arise in the conjucate pairs

As -i is a root, i is also a root

As  -1 + i is a root

And, -1 is also a root

Now the polynomial equation would be

(x + i)(x - i)(x + 1 - i)(x + 1 - i) = 0

(x^2 - i^2)[(x + 1)^2 - i^2] = 0

(x^2 + 1)[(x + 1)^2 + 1] = 0

(x^2 + 1)(x^2 + 2x + 2) = 0

x^4 + 2x^3 + 3x^2 + 2x + 2 = 0