SOLUTION: Please help me, and if u could show me to the answer i would appreciate it muchly. Solve {{{ 6x^4-19x^2+15=0 }}} The solution is x = ???

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me, and if u could show me to the answer i would appreciate it muchly. Solve {{{ 6x^4-19x^2+15=0 }}} The solution is x = ???      Log On


   

Question 359571: Please help me, and if u could show me to the answer i would appreciate it muchly.

Solve

+6x%5E4-19x%5E2%2B15=0+

The solution is x = ???
Found 2 solutions by Alan3354, vleith:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+6x%5E4-19x%5E2%2B15=0+
It doesn't factor, so use the quadratic eqn.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-19x%2B15+=+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=%28-19%29%5E2-4%2A6%2A15=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--19%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+1+%29%29%2F2%5C6+=+1.66666666666667
x%5B2%5D+=+%28-%28-19%29-sqrt%28+1+%29%29%2F2%5C6+=+1.5

Quadratic expression 6x%5E2%2B-19x%2B15 can be factored:
6x%5E2%2B-19x%2B15+=+%28x-1.66666666666667%29%2A%28x-1.5%29
Again, the answer is: 1.66666666666667, 1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-19%2Ax%2B15+%29

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The x is the x^2
x%5E2+=+5%2F3 and 3%2F2
Then x = ± sqrt(5/3) and ± sqrt(3/2)
x = ± sqrt(15)/3 and ± sqrt(6)/2

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
+6x%5E4-19x%5E2%2B15=0+
Let z = x^2
6z%5E2+-+19z+%2B+15+=+0
%283z+-+5%29%282z+-+3%29+=+0
So 3z-5+=+0 or 2z-3=0
Thus z = 5/3 or 3/2
If z is 5/3 then
5%2F3+=+x%5E2 and x=%2B-+sqrt%285%2F3%29 two answers there
If z = 3/2, then 3%2F2+=+x%5E2 and x=%2B-+sqrt%283%2F2%29 two more answers here
see this url for a plot
http://www.wolframalpha.com/input/?i=6x^4-19x^2%2B15%3D0