We have, 4x4−24x3+57x2+18x−45=0 If one the root of the equation is 3+i√6, then the other root be 3−i√6 (x−3+i√6)(x−3−i√6)p(x) =4x4−24x3+57x+18x−45 (x2+9−6x+6)p(x) =4x4−24x3+57x2+18x−45 p(x)=
4x4−24x3+57x2+18x−45
x2−6x+15
IMAGE ∴ p(x)=4x2−3 Product of real roots of the given equation =