It is known that quadratic function f (x) = ax ^ 2 + BX + C and primary function g (x) = - BX, where a, B, C satisfy a > b > C, a + B + C = 0 (a, B, C belong to R) ① Verification: the images of two functions intersect at two different points a and B ② Find the range of the length of the projective A1B1 of line AB on the x-axis

It is known that quadratic function f (x) = ax ^ 2 + BX + C and primary function g (x) = - BX, where a, B, C satisfy a > b > C, a + B + C = 0 (a, B, C belong to R) ① Verification: the images of two functions intersect at two different points a and B ② Find the range of the length of the projective A1B1 of line AB on the x-axis

According to the meaning of the question, let a, B ≠ 0, ∵ a > B > C and a + B + C = 0, ∵ a > 0 and C < 0 (I) Let f (x) = g (x), get AX2 + 2bx + C = 0