Question

if x-3 and x- 1/3 are factors of ax^2+5x+ be, show that a=b

Answer 1

x-3=0
So, x=3
f (3)=a (3)^2+5 (3)+b
9a+15+b=0 --------> 1

x-1/3=0
x=1/3
f (1/3)=a (1/3)^2+5 (1/3)+b
a/9+5/3+b
Taking LCM
a+15+9b/9=0
a+15+9b=0 --------->2

1-2
9a+15+b=0
a+15+9b=0
____________
8a-8b=0 --------->3

When we divide 3rd equation by 8
a-b=0
So a=b
Hence proved.