Find all the roots of the equation x4 - 2x3 + 14x2 - 18x + 45 = 0 given that 1 + 2i is one of its roots.

 All the four roots of the given equation are

Step-by-step explanation:  Given that (1 + 2i) is one of the roots of the following fourth degree polynomial equation:

We are to find all the roots of the above equation.

Since the given equation is of degree 4, so there will be 4 roots of the equation.

We know that the complex roots of any polynomial equation occur in complex conjugate pairs.

Since (1 + 2i) is root of equation (i), so (1 - 2i) is also a root of equation (i).

FACTOR THEOREM : It states that if x = a is a root of the polynomial equation Q(x) = 0, then (x - a) is a factor of the polynomial Q(x).

That is, by factor theorem, we can say

are factors of the polynomial

So, their product is also a factor of the polynomial.

We have

∴ (x² - 2x + 5) is a factor of te polynomial and so we have

Therefore, the other two roots of equation (i) are given by

Thus, all the four roots of the given equation are

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

huh? im pretty sure it is in 199

step-by-step explanation: