Let f (x) = x ^ 2 + X + C (C is greater than 0), if f (x) = 0 has two real roots: x1, X2, (x1 is less than x2) Ask for: 1: The value range of positive real number C 2: Find the value range of x2-x1 3: If there is a real number m such that f (m) is less than 0, we prove that M + 1 is greater than x2

Let f (x) = x ^ 2 + X + C (C is greater than 0), if f (x) = 0 has two real roots: x1, X2, (x1 is less than x2) Ask for: 1: The value range of positive real number C 2: Find the value range of x2-x1 3: If there is a real number m such that f (m) is less than 0, we prove that M + 1 is greater than x2

1 △=1-4c>0
0

The area of the triangle with the vertex of the three intersections of the parabola y = x ^ 2 + 3x + 2 and the coordinate axis is

y=(x+1)(x+2)=0
x=1,x=2
So the point of intersection with X axis (1,0), (2,0)
So the distance between two points is 2-1 = 1
The bottom edge is 1
x=0,y=2
So the point of intersection with the y-axis (0,2), so the height is the distance from the x-axis, which is 2
So area = 1 * 2 / 2 = 1

How to find the area of the triangle enclosed by the function y = 2x-3 and the coordinate axis?

When x = 0, y = - 3
When y = 0, x = 1.5
The area is 3 * 1.5 / 2 = 2.25