Given bi-quadratic equation. f(x)=x4+2x3−16x2−22x+7=0 has one of the root is 2+√3. then one more root will be 2−√3. Now equation whose roots are 2+√3 and 2−√3 is x2−4x+1=0 and so, x2−4x+1 is the factor of bi-quadratic equation x4+2x3−16x2−22x+7=0 ⇒(x2−4x+1)(x2+6x+7)=0 So, (x2−4x+1) and (x2+6x+7) are factors of given bi-quadratic equation. Now, the roots of quadratic equation x2+6x+7=0 aге x=
−6±√36−28
2
=−3±√2 ∴ The roots of given bi-quadratic equations are 2+√3,2−√3,−3+√2 and −3+√2