Find all roots.

1. x^4 - 16x^2 + 63 = 0

Question

Find all roots.

1. x^4 - 16x^2 + 63 = 0

snowsurf · Answer

I won't solve it for you. But lets pick a variable to substitute. Let $$s = x ^{2}$$
and you will have the following equation 

$$s ^{2}-16s+63=0$$

Factor as you normally would then once you done then substitute back x^2 term.

joshoyen · Answer

s=7,s=9

snowsurf · Answer

Very good. So you should have (s-9)(s-7) = 0.

Now put back in the x^2 term.

joshoyen · Answer

(s^2-9)(s^2-7)?

snowsurf · Answer

Yes and set it to zero. Can you factor any more? Take a look at it.

joshoyen · Answer

hm im not sure on that one

whpalmer4 · Answer

@joshoyen you should always think "possible difference of squares" when you see something like $$x^2 - \text{something}$$

remember that the formula for a difference of squares is 
$$(x-a)(x+a) = x^2 +ax -ax - a^2 = x^2 -a ^2$$

snowsurf · Answer

whpalmer4 has a good template for you to figure that last part. Look at the (s^2-9) term.