Question

If both (x-2) and (2x-1) are factors of ax^2+5x+b, show that a-b=0

Answer 1

If (x-2) and (2x-1) are factors, then polynomial will be
(x-2)(2x-1)=0
⇒2x² -x -4x +2=0
⇒2x²-5x +2 =0

Hence, a = 2 and b = 2
so, a-b = 0

Answer 2

Step-by-step explanation:

(x - 2 ) (2x - 1) = 0

2x^2 - x - 4x + 2 = 0

2x^2 - 5x + 2 = 0

a = 2

b = 2

a - b = 2 - 2

= 0