Question

HURRY I NEED HELP!!!!!

State the number of complex roots and the possible number of real and imaginary roots for each equation. Then find all roots, be sure to show all work!
(equations are in the image below)

Answer 1

#1

• (x²+9)(x²+6)=0

First

• x²=-9
• x=±3i

second

• x²=-6
• x=±√6i

4complex roots

#2

• (x²+7)(x²+5)=0

first

• x²=-7
• x=±√7i

Second

• x²=-5
• x=±√5i

4 complex roots

Answer 2

• Both have 4 imaginary roots

Explanation:

1)

• (x^2 + 9)(x^2 + 6) = 0

1.

• x^2 + 9 = 0
• x^2 = - 9
• x = ± √-9
• x = ± 3i

2.

• x^2 + 6 = 0
• x^2 = -6
• x = ±√-6
• x = ± i√6

It has 4 imaginary roots and no real roots

2)

• (x^2 + 7)(x^2 + 5) = 0

1.

• x^2 + 7 = 0
• x^2 = -7
• x = ± √7
• x = ± i√7

2.

• x^2 + 5 = 0
• x^2 = - 5
• x = ± √-5
• x = ± i√5

It has 4 imaginary roots and no real roots