Question

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

Answer 1

$Hey\:There$‼

p(x) = ax² + 5x + b

Given that, ( x – 3 ) and ( x – 1/3 ) are factors of given polynomial.

Therefore, ( x – 3 ) ( x – 1/3 )

= x² + [ 3 + ( 1 / 3 ) ] + 1

= x² + ( 10 / 3 ) x + 1

Now , $Sum\:of\:the\:zeroes$

= – coefficient of x / coefficient of x²

=> –5 / a = 10 / 3

10a = – 5 × 3

a = –15 / 10

a = –3 / 2

$Product\:of\:the\:zeroes$

= constant term / coefficient of x²

=> b / a = 1

a = b

Hence, proved.