Factor the polynomial function over the complex numbers. f(x)=x^3-2x^2+3x-6

1 answer:

6 0

$f(x)=x^3-2x^2+3x-6=x^2(x-2)+3(x-2)=(x-2)(x^2+3)\\\\i=\sqrt{-1}\to i^2=-1\\\\x^2+3=x^2-(-3)=x^2-3i^2=x^2-(\sqrt3)^2i^2)=x^2-(i\sqrt3)^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\boxed{f(x)=(x-2)(x-i\sqrt3)(x+i\sqrt3)}$

You might be interested in

Hep please I need it fast too

kozerog [31]

The value of the expression decreases

4 0

3 years ago

Create triangle A’B’C by reflecting triangle ABC over the y-axis on the coordinate plane. What are the new coordinates of the ve

pickupchik [31]

Answer:

Step-by-step explanation:

When talking about reflection, we usually mean reflecting across a line, or axis. Reflecting a shape means looking at the mirror image on the other side of the axis. Consider the point (x,y), if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:

$(x,y)\rightarrow(-x,y)$

For triangle ABC we have:

$A(-4,2) \\ \\ B(-1,3) \\ \\ C(-1,-4)$

Therefore, the reflecting points are:

$A'(4,2) \\ \\ B(1,3) \\ \\ C(1,-4)$

Both the original triangle and the reflected one are shown below.

8 0

3 years ago

The temperature at 9 p.m. was 12°F. The temperature dropped 15°F by 5 a.m.The temperature at 5 a.m. was

satela [25.4K]

The temperature at 5 am was -3 degrees

12-15=-3

4 0

3 years ago

You and two friends plan to walk your dogs together. You want the meeting place to be the same distance from each person’s resid

AveGali [126]

If we join the points we are gonna end up with a triangle, from there by finding the centroid of the triangle we will get a point which is equidistant from all the three points given in the diagram.

Formula for Centroid:

6 0

2 years ago

The area of a triangular block is 16 squre inches. If the base of the triangle is twice the height, how long are the base and th

klemol [59]

The area of a triangle can be calculated using the formula

1/2 (base) (height)

Let's substitute our known values, letting x represent the value of the height of the triangle.

16 = 1/2* x* 2x

Let's Simplify!

16 = x^2

Finally, lets take the square root of both sides, to get rid of the exponent on the right side of the equation.

x= positive OR negative 4.

However, because x is equal to the height, we know that it can't be negative, so we know that it is positive 4.

The height of the triangle = 4 inches
The base of the triangle = 2h = 8 inches

6 0

3 years ago