Quadratic function f (x) = AX2 + BX + C, (a is a positive integer), C ≥ 1, a + B + C ≥ 1, equation AX2 + BX + C = 0 has two unequal positive roots less than 1, then the minimum value of a is______ ．

Quadratic function f (x) = AX2 + BX + C, (a is a positive integer), C ≥ 1, a + B + C ≥ 1, equation AX2 + BX + C = 0 has two unequal positive roots less than 1, then the minimum value of a is______ ．

Let f (x) = a (X-P) (X-Q), where P and Q belong to (0, 1) and P is not equal to Q. from F (0) ≥ 1 and f (1) ≥ 1, we can get Apq ≥ 1, a (1-p) (1-Q) ≥ 1. The multiplication of the two formulas has A2p (1-p) Q (1-Q) ≥ 1, that is, A2 ≥ 1p (1 − P) Q (1 − q), and we can know P (1-p) Q (1

If the quadratic function f (x) = AX2 + BX + C, C > = 1, a + B + C > = 1 and the equation has two unequal positive roots less than 1, then the minimum value of a is?
This is the question for the third month of senior high school in Longwan middle school

When x = 1, f (1) = a + B + C > = 1. When x = 0 is, f (0) = C > = 1. And both of them are between [0,1]. You can draw a picture. It is obvious that a is positive. The value of a determines the opening of the parabola. The limit of the problem is that the parabola passes through (0,1) point and (1,1) point

Quadratic function f (x) = AX2 + BX + C, (a is a positive integer), C ≥ 1, a + B + C ≥ 1, equation AX2 + BX + C = 0 has two unequal positive roots less than 1, then the minimum value of a is ()
A. 2B. 3C. 4D. 5

Let f (x) = a (X-P) (X-Q), where P and Q belong to (0, 1) and P is not equal to Q. from F (0) ≥ 1 and f (1) ≥ 1, we can get Apq ≥ 1, a (1-p) (1-Q) ≥ 1, and the multiplication of the two formulas has A2p (1-p) Q (1-Q) ≥ 1, that is, A2 ≥ 1p (1 − P) Q (1 − q), and from the basic inequality, we can get P (1-p)

Given the range of quadratic function f (x) = ax ^ 2 + 2x + C (x ∈ R) [0, positive infinity], f (2 + x) = f (2-x), then f (1) is

Range [0, positive infinity],
Discriminant = 4-4ac = 0 AC = 1
F (2 + x) = f (2-x) axis of symmetry x = 2 - 1 / a = 2 a = - 1 / 2
c=-2
f(1)=-1/2+2+2=7/2