Question

If (x-3) and (x-1/3) are both factors of ax²+5x+b, than show a=b

Answer 1

Hi mate !!

$given \: \: equ \: = a {x}^{2} + 5x + b$

It is given that ( x - 3 ) and ( x - 1/3 ) is the factor of given equation.

So , x = 3 and x = 1/3 are the zeros of given equation !!

We know that ,

$product \: of \: zeros \: = \frac{constant \: term}{coefficient \: of {x}^{2} }$

and here , constant term is b and coefficient of x ^2 is a

So ,

$3 \times \frac{1}{3} = \frac{b}{a}$

1 = b/a

a = b

Hence , proved !!