It is known that a, B and C are all positive integers, and the parabola y = AX2 + BX + C has two different intersections A and B with the x-axis. If the distance from a and B to the origin is less than 1, Finding the minimum of a + B + C

It is known that a, B and C are all positive integers, and the parabola y = AX2 + BX + C has two different intersections A and B with the x-axis. If the distance from a and B to the origin is less than 1, Finding the minimum of a + B + C

Let the coordinates of a and B be (x1,0), (x2,0), and X1 < X2, then X1 and X2 are two parts of the equation AX ^ 2 + BX + C = 0. According to Weida's theorem, X1 + x2 = - B / A0 ∵ x1, the distance from X2 to the origin is less than 1, so the absolute value of X1 is less than 1, and the absolute value of X2 is less than 1 ∵ C / a = x1x2 < 1, that is, C < A, when x = 0, y = C > 0, when x = - 1, y = A-B + C >

It is known that the parabola y equals 3ax2 plus 2bx plus C. (1) if a equals B equals 1 and C equals - 1, find the coordinates of the common point of the parabola and X axis
It is known that the parabola y equals 3ax2 plus 2bx plus C. (1) if a equals B equals 1 and C equals - 1, find the coordinates of the common point of the parabola and X axis. (2) if a equals B equals 1 and X is greater than - 1 and less than 1, the parabola and X axis have and only have one common point, and find the value range of C

1. Y = 3x2 + 2x-1, let y = 0, then 3x2 + 2x-1 = 0, x = 1 or x = - 1 / 3
2.y=3x2+2x+c,-1