The image of quadratic function y = x ^ 2 - (a + 2) x + 2A (a > 0) intersects with X-axis at two points a and B, intersects with Y-axis at C, and the area of △ ABC is 3~

The image of quadratic function y = x ^ 2 - (a + 2) x + 2A (a > 0) intersects with X-axis at two points a and B, intersects with Y-axis at C, and the area of △ ABC is 3~

Let the two intersections of X axis be x1, X2, then let y = 0 have x1, X2 are two of the equation y = 0, so X1 + x2 = a + 2, X1 * x2 = 2A, so | ab | = | x1-x2 | = square root (x1 + x2) ^ 2-4 * X1 * x2 = | A-2 | the high OC of triangle = | 2A | (let x = 0), so the area is 3 = 1 / 2 * | A-2 | 2 * a |