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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

4x%5E3-8x%5E2=0 Start with the given equation


4x%5E2%28x-2%29=0 Factor out the GCF 4x%5E2


4x%5E2=0 or x-2=0 Set each factor equal to zero


x=0 or x=2 Solve for "x" in each case


So the solutions are x=0 or x=2






# 2

5x%5E2-3x%2B6=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=5, b=-3, and c=6


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%286%29+%29%29%2F%282%285%29%29 Plug in a=5, b=-3, and c=6


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%286%29+%29%29%2F%282%285%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%285%29%286%29+%29%29%2F%282%285%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9-120+%29%29%2F%282%285%29%29 Multiply 4%285%29%286%29 to get 120


x+=+%283+%2B-+sqrt%28+-111+%29%29%2F%282%285%29%29 Subtract 120 from 9 to get -111


x+=+%283+%2B-+sqrt%28+-111+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%283+%2B-+i%2Asqrt%28111%29%29%2F%2810%29 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...


x+=+%283%2Bi%2Asqrt%28111%29%29%2F%2810%29 or x+=+%283-i%2Asqrt%28111%29%29%2F%2810%29 Break up the expression.


So the answers are x+=+%283%2Bi%2Asqrt%28111%29%29%2F%2810%29 or x+=+%283-i%2Asqrt%28111%29%29%2F%2810%29


which approximate to x=1.354%2Ai or x=-0.754%2Ai


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) About Me  (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
= %283%2F10%29+%2B-+sqrt%28-111%29%2F10
= 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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-3x%2B6+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A5%2A6=-111.

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 - sqrt%28+111%29+=+10.5356537528527.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-3%2Ax%2B6+%29