Question

if both x-2 and 2x-1 are factors of ax2+5x+ab show that a-b=0​

Answer 1

Answer:

a-b is not equal to zero

Step-by-step explanation:

let

ax2+5x+ab =f(X)

given both (x-2)and(2x-1) are factors,

so,

1/2 and 2 are roots,

so,sum of roots=5/2=-5/a {since,sum of roots in

a=-2 ax2+bx+c is( -b/a)}

product of roots=1=b. {since,product of

roots inax2+bx+c is

(c/a)}.

a=-2,b=1;a-b is not equal to zero

Answer 2

Step-by-step explanation:

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