PART A: CHOOSE 2 From this Part! State the number of complex roots and the possible number of real and imaginary roots for each equation. Then find all roots.

Question

1) x 2 (x + 2)(x - 5) = 0 3) (x 2 + 7)(x 2 + 5) = 0

2) (x 2 + 9)(x 2 + 6) = 0 4) (x - 2)(x + 2)(x 2 + 4) = 0

Answer 1

Hi,

1) x 2 (x + 2)(x - 5) = 0 every parenthesis must be equal zero then find the answer-------> 0, -2, 5

3) (x 2 + 7)(x 2 + 5) = 0 the same

x 2 + 7 = 0 -----> x^2 = -7 root of both side --------> x = ±√7 i

x 2 + 5 = 0 ------> x^2 = -5 root of both side --------> x = ±√5 i

this equation has 4 complex roots

2) (x 2 + 9)(x 2 + 6) = 0

Exactly the same and complex answers will be x = ± 3i and ±√6 i

4) (x - 2)(x + 2)(x 2 + 4) = 0

x - 2 = 0 ------> x = 2 real

x + 2 = 0 ------> x = -2 real

x^2 + 4 = 0 -----> x^2 = -4 ----> x = ±2 i imaginary root

I hope it is useful.

Minoo