Consider all the real roots of the equation x^4-10 x^2+9=0 . What is the sum of the absolute values of the roots?

Step-by-step solution

aligned & x^4-10 x^2+9=0 & x^4-9 x^2-x^2+9=0 & x^2 (x^2-9 )-1 (x^2-9 )=0 & (x^2-9 ) (x^2-1 )=0 & x^2-9=0 or x^2-1=0 & x= 3 or x= 1 aligned Sum of the absolute values of the roots =3+(-3)+1+(-1)=8