Question

find the value of a and b if x-1 and x-2 are factors of x×x-ax+b

Answer 1

p(x)=x^2-ax+b
g(x)=x-1=0
g(x)=x=1
p(1)=(1)^2+a(1)+b=0
=1-a+b=0
-a+b=-1................{1}
p(x)=x^2-ax+b
g(x)=x-2=0
x=2
p(2)=(2)^2-a(2)+b=0
4-2a+b=0
-2a+b=-4..........{2}
subtract 1 from 2
-2a+b=-4
-a+b=-1
______
-a=-3
a=3
substitute a=3 in eq.(1)
-3+b=-1
b=2