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

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles