Let f (x) = the square of AX + BX + C (a > 0) and f (1) = A / 2 (1)) prove that the function has two zeros

Let f (1) = A / 2 = > A / 2 = a + B + C = > - B = A / 2 + CB & sup2; - 4ac = A & sup2; + 4 + C & sup2; + ac-4ac = A & sup2; + 4 + C & sup2; - 3aca & sup2; - 4 + 9A & sup2; / 4-9a & sup2; = - 2A & sup2; + (3a / 2-C) & sup2; depend on whether the title is wrong

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1. If the image of function y = A-X / x-a-1 is symmetric with respect to point (4, - 1), what is the value of real number a?
2. If the function f (x) has f (a + x) = - f (A-X) for all real numbers in the domain of definition, then the image f (x) of the function is a centrosymmetric graph whose center of symmetry is
3. Given that the function f (x) = x + m / x, and the function image passes through the point (1,5), what is the value of the real number m
4. If the function f (x) defined on R is an odd function with period 2, then the equation f (x) = 0 has at least several real roots on [- 2,2]? Please explain in detail
5. Let m be a set of functions f (x) which satisfy the following properties: in the domain of definition, in x0, f (x0 + 1) = f (x0) + F (1) holds. The following functions are known: ① f (x) = 1x; ② f (x) = 2X; ③ f (x) = LG (x2 + 2); ④ f (x) = cos π x, where the function belonging to the set M is () A. ①③B. ②③C. ③④D. ②④
6. It is known that a set M is a set of all functions f (x) which satisfy the following properties: for function f (x), any two different independent variables X1 and X2 in the domain of definition have | f (x1) - f (x2) | ≤| x1-x2 | (1) judge whether the function f (x) = 3x + 1 belongs to set M? (2) if G (x) = a (x + 1 x) belongs to m on (1, + ∞), find the value range of real number a
7. It is known that M is a set of all functions f (x) satisfying the following properties. For function f (x), Let f (x) be a set of any two self-sufficient functions in the domain of F (x) It is known that M is a set of all functions f (x) satisfying the following properties (x) For any two independent variables X 1.x 2 in the domain, | f (x 1) - f (x 2) | ≤| x 1-x 2 | holds 1. Given that the function g (x) = ax ^ 2 + BX + C belongs to m, write the conditions that real numbers a, B, C must satisfy 2. For the element H (x) = √ (x + 1) of set M, X ≥ 0, find the minimum value of constant K satisfying the condition
8. If the function f (x) satisfies f (x + 3) = f (- x + 5) in its domain of definition, and the equation f (x) = 0 has five unequal real roots, find these five roots Find the sum of the five real roots
9. Given the function f (x) = (x ^ 2-3x-2) g (x) + 3x-4, where g (x) is a function whose domain is r, it is proved that the equation f (x) = 0 must have real roots in (1,2)
10. Function f (x) is defined as R, satisfying f (x) = f (14-x), equation f (x) = 0 has n real roots, the sum of these n roots is 2009, then n is to process, fast
11. If the two zeros of the function f (x) = xsquare - ax-b are 2 and 3, find loga25 + B2
12. If the zeros of the function f (x) = xsquare-b are 2 and 3, try to find the zeros of the function g (x) = bsquare-ax-1
13. Given the function y = ax & # 178; + BX + C, if AC < 0, then the number of zeros of function f (x) is
14. Given the quadratic function f (x) = AX2 + BX + C, if f (x) + F (x + 1) = 2x2-2x + 13 (1), find the analytic expression of function f (x); (2) draw the image of the function; (3) find the maximum value of function f (x) when x ∈ [T, 5]
15. It is known that the quadratic function f (x) = ax & # 178; + BX + 1 and G (x) = (BX-1) / (A & # 178; X + 2b). When B = 2A, ask if there is a value of x such that any real number a satisfying - 1 ≤ a ≤ 1 and a ≠ 0 holds the inequality f (x) < 4? And explain the reason
16. It is known that the quadratic function f (x) = AX2 + BX + C satisfies a > b > C, f (1) = 0. The function g (x) = f (x) + BX (1) proves that the function y = g (x) must have two different zeros (2) Let the two zeros of function y = g (x) be x1, X2, and find the absolute value range of x1-x2
17. The increase and decrease of quadratic function f (x) = AX2 + BX + C (a < 0) in the interval [- B2A, + ∞) is judged and proved according to the definition
18. (urgent! Just finished! Quadratic function f (x) = ax ^ 2 + BX + C (a)
19. It is known that a, B and C are positive integers, and the quadratic function y = AXX + BX + C. when x is greater than or equal to - 2 and less than or equal to 1, y is larger If y is greater than or equal to - 1 and less than or equal to 7, find the analytic expression of quadratic function
20. What is the condition that the quadratic function y = AXX + BX + C (a is not equal to 0) is always negative "AXX" is a times the square of X