Expert: Bobby Soltani - 4/20/2006

Question
This is from an assignment and it is killing me i just can't figure it out. i have worn my book out searching for like examples. sorry but i can't figure out how to type the exponents in.
the instructions are to solve by any means and the question is.
-10xto the 4 - 7x to the 2 + 12 =0
thanks
Jon

Answer
Hi Jonathan,

I'll represent the exponents using the ^ sign.  For instance, x squared will be x^2.

-10x^4 - 7x^2 + 12 = 0

Using trial and error, this can be factored into the following.

(-5x^2 + 4)(2x^2 + 3) = 0

Now, we can solve each quadradic to get all 4 roots.

-5x^2 + 4 = 0

-5x^2 = -4

x^2 = 4/5

x = +-2/SQRT(5)

2x^2 + 3 = 0

2x^2 = -3

x^2 = -3/2

the other two roots are imaginary.

I hope this helps.

Bobby