The other two roots are (1−√2) and (2+i) . [∵ these roots occur in conjugate pair] ∴x4+bx3+cx2+dx+e =[x2−{(1−√2)+(1+√2)}x+(1−√2)(1+√2)] x[x2−{(2−i)+(2+i)}x+(2−i)(2+i)] =(x2−2x−1)(x2−4x+5) =x4−6x3+12x2−6x−5 ⇒b=−6,c=12,d=−6 Now, the given quadratic equation becomes. i.e −6x2+12x−6=0 x2−2x+1=0 (x−1)2=0 Hence, the roots are real and equal.