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

another three roots are 1-2i, 3i ,-3i

Step-by-step explanation:

has one root = 1+2i

then another root will be  = 1-2i  [ since complex roots always occurs in pair]

therefore    together both roots makes function as

since this polynomial is formed by its roots so it must divide the parent polynomial therefore  on dividing the parent  polynomial  by obtained polynomial, we get

therefore we have three  other roots are

1-2i

-3i

3i

The area of the rectangle would be (11)(7) =77

The area of the square is (6)(6)=36

77+36=113

Hope this helped :)