Question

x^4 - 5x^2 - 14 = 0 substitute u for x^2
I dont understand how to solve this one

Answer 1

x^4 is really (x^2)^2 so you would end up with u^2-5u-14=0

Answer 2

\[(x^2)^2 - 5x^2 - 14 = 0\]\[x^2 = u\]\[u^2 - 5u - 14 = 0\]

Answer 3

awesome thank you. I was confused

Answer 4

its simply becomes a quadratic

\[u^2 - 5u - 14 = 0\]

solve by factoring

then let x^2 = the solutions you get for u

Answer 5

Great thank you very much ^_^

Answer 6

If u = x^2, then u^2 = x^4

So your equation is just u^2 -5u - 14 = 0
Factor this, (u-7)(u+2) = 0
so, u = 7 and u = -2

Now, since u = x^2, so x^2 = 7 , then x = +/- sqrt(7)
If u = - 2, then x^2 = -2, x = +/- sqrt (-2) = +/- i sqrt(2)