Factor to find all the zeros x^3-5x^2+16x-30=0

factors of 30:

1,2,3,5,15,30
of which we'd determine that x=3 is a solution such that
x^3-5x^2+16x-30=(x-3)(x^2-2x+10)=0
but the quadratic is not factorable over the reals - so we'd need the quadratic formula to determine that x=1+3i, and x=1-3i are the other two factors. Thus the zeros are:
{3, 1-3i, 1+3i}

how many pounds of coffee worth $10 a pound should be added to 20 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound?

10x+4(20)=5(x+20)
10x+80=5x+100
5x=20
x=4

4 pounds

A rectangular prism is 10 centimeters long and 5 centimeters wide. The volume of the rectangular prism is 400 cubic centimeters. What is the heights of the rectangular prism?

height is 8cm

Solve the following equation: x(2i+3j+k).(i+j+x k)=6

Assuming x is a variable, and you want a dot product, then...





x=6 or x=1

If 'a' and 'b' both are unit vectors then how it is possible that 'a+b' is also a unit vector?

The conditions needed are:
1)

2)



3)


This nonlinear system does have solutions, for example


is such a pair

Find the general formula for : a) 1, -1/3,1/5,-1/7 .... , b) -1/2, 3/2,-5/2, 7/2....

a)

b)

Solve the absolute value equation: ||2x+1|-18|=4

The easiest way to solve any absolute value problem is to determine all possible equations with respect to the signs of the expressions. This equation has 4 possibilities: 


case 1)
2x+1-18=4 
2x=21
x=21/2 

case 2)
-2x-1-18=4
-2x=23
x=-23/2 


case 3)
2x+1-18=-4
2x=13
x=13/2 

case 4)
-2x-1 -18=-4
-2x=15
x=-15/2