Question

If x+2 , is h.c.f of ax square-bx-c and bx square-axsquare+c. Prove a=b .

Answer 1

if x + 2 is HCF of [tex]a x^{2} - b x -c \ \ and \ \ b x^{2} - a x + c \\ [/tex]

it means that x = -2 is  a root of the quadratic expressions and if you substitute x = -2 in the above expressions, their value is zero.

$4 a + 2b - c = 0 \\ 4b +2 a +c = 0$

Add the two equations. we get

$6 a + 6 b + 0 c = 0 \\ 6 a = - 6b \\ a = -b$