SOLUTION: Hello, I just want to doublecheck my answers if someone can help me. Solve the following for x (use quadratic equation or factor out): 4x^3-8x^2=0 My answer was that there

Question 192184: Hello,
I just want to doublecheck my answers if someone can help me.
Solve the following for x (use quadratic equation or factor out):
4x^3-8x^2=0
My answer was that there are No solutions to this problem
The other problem was:
5x^2-3x+6=0
My answer was the following:
using the quadratic equation I came out with
3-+SQRT(-3)^2-4(5)(6)/2(5)
= 3-+SQRT111/10
Since the SQRT of 111 is 10.525 it would not be a R number, thereby No solution either.
Please let me know if I have that right; it would be greatly appreciated.
Thank you,
Gryhd
Found 3 solutions by jim_thompson5910, Alan3354, edjones:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
# 1

Start with the given equation

Factor out the GCF

or Set each factor equal to zero

or Solve for "x" in each case

So the solutions are or

# 2

Start with the given equation.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root. Note: if you have no clue what the term "i" is (ie you haven't learned about it yet), then this means that the answer is simply "no solutions"

If you know what "i" is, then...

or Break up the expression.

So the answers are or

which approximate to or

Note: Once again, if you have no clue what the term "i" is (ie you haven't learned about it yet), then this means that the answer is simply "no solutions"

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve the following for x (use quadratic equation or factor out):
4x^3-8x^2=0
4x^2*(x-2) = 0
x = 0
x = 2
----------------------
The other problem was:
5x^2-3x+6=0
My answer was the following:
using the quadratic equation I came out with
3-+SQRT(-3)^2-4(5)(6)/2(5)
= 3-+SQRT111/10
=
= 0.3 +i*sqrt(111)/10
= 0.3 -i*sqrt(111)/10
No real number solutions.
-------------------
Since the SQRT of 111 is 10.525 it would not be a R number, thereby No solution either.
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
4x^3-8x^2=0
4x^2(x-2)=0
x=0, x=2
.
5x^2-3x+6=0
There is no real number answer.
.
Ed
.

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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 : .

The discriminant -111 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -111 is + or - .

The solution is , or
Here's your graph:

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