The given quadratic equation is,
3x4−13x2+10=0
3(x2)2−13(x2)+10=0
Substituting x2=m we get
3m2−13m+10=0
3m2−3m−10m+10=0
3m(m−1)−10(m−1)=0
(m−1)(3m−10)=0
m−1=0 or 3m−10=0
∴ m=1 or 3m=10
∴ m=1 or m=103
Substituting m=x2, we get
x2=1 or x2=103
x=±1 or x=±√103
∴ x=1,−1,√103,−√103
1,−1,√103 and −√103 are the roots of the given quadratic equation.