Solve the equation exactly in the complex number system. x^3+4x^2+9x+36=0

1 answer:

5 0

Factor by grouping.
0 = (x^3 +4x^2) +(9x +36) = x^2(x+4) +9(x+4) = (x^2+9)(x+4)

The first factor is the difference of squares (in complex numbers), so the form for factoring that can be used:
a^2 - b^2 = (a -b)(a +b)
Here, a=x, b=3i.

Then the factorization in complex numbers is
0 = (x -3i)(x +3i)(x +4)
Solutions are the values of x that make these factors be zero.

x = -4, -3i, 3i

You might be interested in

A square rectangle has a length of 9.00 inches and a width of 4.25 inches. What is the area in square inches? Round to the corre

nika2105 [10]

Answer:

38.3

Step-by-step explanation:

multiply l x w to get your answer then just round. Hope it helps!!

6 0

3 years ago

What is the volume of a cylinder if the radius is 3.2 centimeters and the height is 5 centimeters

Illusion [34]

Answer:

Step-by-step explanation:

Volume of cylinder: V = π×r² × h

r = 3.2 cm

h = 5 cm

Volume:

V = π×(3.2)²×5 = 51.2π cm³ = 160.8495.... cm³ ≈ 160.85 cm³

6 0

2 years ago

Which one or ones of the following statements is/are true?

EastWind [94]

Only the first statement is true.

3 0

2 years ago

A to the 5th power times a to the -3 power

olasank [31]

A to the second power is the answer to this problem

8 0

3 years ago

The area of the base of a rectangular prisim four and three fourths and the height of two and one third what is the volume

VikaD [51]

Data:
$A_{base} = 4 \frac{3}{4} = \frac{4*4+3}{4} = \frac{16+3}{4} \to A_{base} = \frac{19}{4}$

$h (height) = 2 \frac{1}{3} = \frac{3*2+1}{3} = \frac{6+1}{3} \to h (height) = \frac{7}{3}$
$v (volume) = ?$

Formula: $V = A_{b}*h$

Solving:
$V = A_{b}*h$
$V = \frac{19}{4} * \frac{7}{3}$
$V = \frac{133}{12}$
$V = 11.08333....$
$\boxed{\boxed{V \approx 11.08}}\end{array}}\qquad\quad\checkmark$

7 0

3 years ago