Question

if both
(x-2) and (2x-1) are factors of
$a {x}^{2} + 5x + b$
show that a-b=0

Answer 1

Hey here is your answer
________________________

if both
(x-2) and (2x-1) are factors of
$a {x}^{2} + 5x + b$....( 1 )

then
( x-2 ) × ( 2x-1 )=$2 {x}^{2} + 5x + 2$...( 2 )
is also the factor of
$a {x}^{2} + 5x + b$

Now by comparing equation 1. and 2. we get :

$a {x}^{2} + 5x + b$ = $2 {x}^{2} + 5x + 2$

$a {x}^{2} + b$ = $2 {x}^{2} + 2$

a = 2 ( coefficient of ${x}^{2}$ )
b = 2 ( constant term )

Now,
= a - b
= 2 - 2
= 0......proved
_________________________

Hope it may helpful to you
plzz mark me as brainlist.

Answer 2

hope this helps u .thanks for asking this question.