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

1 answer:

6 0

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

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Find the length of a rectangle if its

Alina [70]

Answer: L = 29cm

Step-by-step explanation:

Let's go!!

To find any rectangle area, you have to apply this formula: A = L . w , where L is the length and w is the width.

So, we have w = L - 13 (the width is 13 less than the Length) and then, perimeter is 90 cm.

Well, I hope you remember that the perimeter of rectangle is 2L + 2W. In this case, 2L + 2w = 90

Then, you might to solve this system of equation:

2L + 2w = 90

w = L - 13

Simplifying the first equation, you'll have L + w = 45 (you can divide everything of 2).

Our new system:

L + w = 45

w = L - 13

Using the substituition method:

L + L - 13 = 45

2L = 58

L = 29 cm

the width is 29 - 13 = 16 cm

4 0

4 years ago

How do you do this problem? Please explain.

horrorfan [7]

Answer: 8.632

<u>Step-by-step explanation:</u>

First, you need to find the length of AE. Since ΔAEC is a right triangle, we can use:

$sin\ C=\dfrac{AE}{AC}\\\\\\sin\ 50 = \dfrac{AE}{5}\\\\\\5\ sin\ 50=AE\\\\3.83=AE$

Next, Use Heron's formula to find the Area of ΔADE.

AE = 3.83
ED = 6
AD = 9

Heron's formula is:

$A=\sqrt{s(s-a)(s-b)(s-c)}\quad \text{where}\ s = \dfrac{a+b+c}{2}\\\\s=\dfrac{AE+ED+AD}{2}=\dfrac{3.83+6+9}{2}=\dfrac{18.83}{2}=9.415\\\\A=\sqrt{9.415(9.415-3.83)(9.415-6)(9.415-9)}\\\\.\quad=\sqrt{9.415(5.585)(3.415)(0.415)}\\\\.\quad=\sqrt{74.519}\\\\.\quad=8.632$