Mathematics Quadratics

How does one solve a quadratic with powers higher than 2?
For example, this question -
Find all the real roots of the following function -
f(x) = x^6 + 9x^3 + 8

(Original post by Notnek)There isn't one method for finding the roots of higher degree polynomials but this particular one can be solved by thinking of it like this

$(x^3)^2 + 9(x^3) + 8=0$

So this is a quadratic in terms of $x^3$ or you can make a substitution $y=x^3$ to see that more clearly:

$y^2+9y+8=0$

Can you continue from here?

This is sometimes known as a hidden quadratic and you'll need to get used to spotting them.

I used the method you suggested - from it I got the roots of - 8 and -1, but in the answers section it mentions the answer as -2 and -1?