SOLUTION: 1. x^3+216=0 2. 5x^3+30x^2+45x=0 3. 1/x^2+8/x+15=0

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Question 213777: 1. x^3+216=0


2. 5x^3+30x^2+45x=0


3. 1/x^2+8/x+15=0
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
1. x^3+216=0

Subtracting 216 from both sides of equation



Answer

2. 5x^3+30x^2+45x=0





where we have x=0, 5x+15=0 and x+3=0. Solving yields

x=0, x=-3 and x=-3, or solve quadratic equation using following steps,

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: -3, -3. Here's your graph:




3. 1/x^2+8/x+15=0 Multiply by x^2 to get rid of denominator







where we have 5x+1=0 and 3x+1=0. Solving yields

So x=(-1/5) and x=(-1/3)

We can also use the quadratic formula as follows:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -0.2, -0.333333333333333. Here's your graph:



I hope the above steps were helpful.

And good luck in your studies!

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Respectfully,
Dr J
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