Question

Please help!!

Answer 1

Because this is a fourth degree that will be tricky to factor as it is, we will do a u substitution. Let $x^2=u$. We can now rewrite that polynomial in terms of u: $u^2-7u-8=0$. Filling into the quadratic formula we have $u=\frac{7+/-\sqrt{49-4(1)(-8)}}{2}$. Simplifying down $u=\frac{7+/-\sqrt{81}}{2}$ and $u=\frac{7+9}{2}$ or $u=\frac{7-9}{2}$. That means that u = 8 or u = -1. But don't forget that we let $u=x^2$, so we have to put x-squared back in for u. That gives us $x^2=8$ which simplifies down to $+/-2\sqrt{2}$. That also gives us $x^2=-1$. When we take the square root of -1, we have to use the fact that -1 = i^2, so we sub that in to get $x=+/-i$. All in all, your solutions are as follows: $2\sqrt{2},-2\sqrt{2},i,-i$ which is choice b.