Given, 2-i is one of the roots of the equation x4−9x3+31x2−49x+30=0 As coefficient of x4,x3,x2,x and constant are real numbers and 2−i is one of the root, then 2+i is the another root of the equation. (x−2−i)(x−2+i)=0 ⇒(x−2)2−i2=0⇒x2−4x+4+1=0 ⇒x2−4x+5=0