Based on the fundamental theorem of algebra, how many complex roots does each of the following equations have? write your answer as a number in the space provided. for example, if there are twelve complex roots, type 12. x(x2 - 4)(x2 + 16) = 0 has a0 complex roots (x 2 + 4)(x + 5)2 = 0 has a1 complex roots x6 - 4x5 - 24x2 + 10x - 3 = 0 has a2 complex roots x7 + 128 = 0 has a3 complex roots (x3 + 9)(x2 - 4) = 0 has a4 complex roots

According to the fundamental theorem of algebra, every polynomial of degree n has n complex zeroes.

Part A:

Given



Thus, the given polynomial is of degree 5 and hence has 5 omplrex roots.

Part B:

Given



Thus, the polynomial is of degree 4 and hence has 4 complex roots.

Part C:

Given



Thus, the given polynomial is of degree 6 and hence has 6 complex roots.

Part D:

Given



Thus, the given polynomial is of degree 7 and hence has 7 complex roots.

Part E:

Given



Thus, the given polynomial is of degree 5 and hence has 5 complex roots.

In the first triangle 80+20+p=180 (since sum of all angles of a triangle is 180)so p= 80also in second triangle 55+45+q=180 (since sum of all angles of a triangle is 180)so q=80so we can conclude that p=80 degrees q=80 degrees so p=q=80 degreeshence option b is correct

Ithink the answer is a