Question

If (x-3) and (x-1/3) are both factors of ax^2+5x+b,then show that a=b

Answer 1

ax^2+5x+b = 0
(x-3)   and  (x-1/3) are the factors of the equation ax^2+5x+b=0
now put the values of x in the equn.
when x=3
a3^2 + 5*3+b=0
or, 9a+b=-15-------eqn(1)
when x= 1/3
a/9+5/3+b=0
a+9b=-15--------------eqn(2)
from (1) & (2)
a+9b=9a+b
-8a=-8b
a=b

Answer 2

ax^2+5x+b = 0

(x-3)   and  (x-1/3) are the factors of the equation ax^2+5x+b=0

now

when x=3

a3^2 + 5*3+b=0

or, 9a+b=-15-------eqn(1)

when x= 1/3

a/9+5/3+b=0

a+9b=-15--------------eqn(2)

from (1) & (2)

a+9b=9a+b

-8a=-8b

a=b

Hence PROVED

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