Roots of x2−5x+4 are x=1 and x=4. Substitute x=1 in x4−px2+q=0 ⇒14−p(12)+q=0 ⇒1−p+q=0 ⇒q=p−1−−−−(1) Substitute x=4 in x4−px2+q=0 ⇒44−p(42)+q=0 ⇒256−16p+q=0 ⇒q=16p−256 Equate q values from 1 and 2 ⇒p−1=16p−256 ⇒255=15p ⇒p=17 Substitute p=17 into q=p−1 ⇒q=17−1 ⇒q=16 ∴ The values of p and q are 17 and 16 respectively.
