Question

All real and complex roots

Answer 1

`\large\boxed{x=-3-√(17)\ \vee\ x=0\ \vee\ x=-3+√(17)}`

Explanation:

`t(x)=x^4+6x^3-8x^2\\\\t(x)=0\iff x^2(x^2+6x-8)=0\iff x^2=0\ \vee\ x^2+6x-8=0\\\\x^2=0\to\boxed{x=0}\\\\x^2+6x-8=0\qquad\text{add 8 to both sides}\\\\x^2+2(x)(3)=8\qquad\text{add}\ 3^2\ \text{to both sides}\\\\x^2+2(x)(3)+3^2=8+3^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+3)^2=8+9\\\\(x+3)^2=17\to x+3=\pm√(17)\qquad\text{subtract 3 from both sides}\\\\\boxed{x=-3-√(17)}\ \vee\ \boxed{x=-3+√(17)}`