Solve 2x^4 + 16x² + 24 = 0. Find all complex zeros and show your work.

Answer 1

This is a quadratic equation in x^2, so we wil solve it like a quadratic. To see it easier, you can call x^2=y.

So, we need to solve 2y^2+16y+24=0

First, you can divide the entire equation by 2:

y^2+8y+12=0

This can be either factored out or you can apply the quadratic formula.

To factor out, you look for two numbers that multiplied gives you 12 and added makes -8, which are -6 and -2.

Therefore (y+6)(y+2)=0.

Since the equation was in x, go back to x^2=y.

x^2=-6 and x^2=-2.

In complex numbers: x^2=6i^2 and x^2=2i^2, therefore there are four complex solutions:

x=+i 6^0.5 (square root of 6=6^0.5), x=-i 6^0.5, x=+i 2^0.5, and x= -i 2^0.5