Question

x-2 and x-1 factors of px2-rx+8 then p2+r2=

Answer 1

for factor x-2
p*2² -r*2+8=0
=>4p-2r=-8
=>2p-r=-4----------(1)
for factor x-1
p1² -r*1+8=0
=>p-r=-8---------(2)
(1)-(2)==>
2p-r-p+r=-4+8
=>p=4
putting the value of p in eqn(2)
4-r=-8
=>r=12
now, p² +r² =4² +12² =16+144=160