SOLUTION: please help me find the find real solution to {{{2x^4-5x^2-12=0}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: please help me find the find real solution to {{{2x^4-5x^2-12=0}}}      Log On


   

Question 366752: please help me find the find real solution to 2x%5E4-5x%5E2-12=0
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E4-5x%5E2-12=0
..
2x%5E4-8x%5E2%2B3x%5E2-12=0
..
2x%5E2%28x%5E2-4%29%2B3%28x%5E2-4%29=0%29
..
%28x%5E2-4%29%282x%5E2%2B3%29=0
%28x%2B2%29%28x-2%29%282x%5E2%2B3%29=0
..
x=-2,2
...
m.ananth@hotmail.ca

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E4+-+5x%5E2+-+12=0
z+=+x%5E2
2z%5E2+-+5z+-+12+=+0
Use quadratic formula
z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+2
b+=+-5
c+=+-12
z+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2+-+4%2A2%2A%28-12%29+%29%29%2F%282%2A2%29+
z+=+%28+5+%2B-+sqrt%28+25+%2B+96+%29%29%2F4+
z+=+%28+5+%2B-+sqrt%28+121+%29%29%2F4+
z+=+%285+%2B+11%29%2F4
z+=+4
and
z+=+%285+-+11%29%2F4
z+=+-3%2F2
And since z+=+x%5E2,
x%5E2+=+4
x+=+2
x+=+-2
These are the real solutions
z+=+-3%2F2 gives 2 imaginary solutions