Inequality ax ^ 2 + ax + A-1 I think we should discuss the scope of X

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• 1. 1. If the univariate quadratic equation x2 + ax + 1 ≥ 0 holds for all real numbers x, find the value range of real number A. (what is △ at this time?) For all real numbers x, the inequality AX2 + 4x + a ＞ 1-2x2 holds, and the value range of real number a is obtained Ask specific process.. the teacher did not speak carefully And when △ why is constant established? Is constant meaningful?
• 2. Given that the equation AX ^ 2 + BX-1 = 0 (AB belongs to R and a > 0) has two real roots, one of which is in the interval (1,2), what is the value range of A-B The answer is (- 1, positive infinity). I want a simple and understandable solution
• 3. Given the mapping f a → B, a = b = R, the corresponding rule is: X → y = - x2 + 2x, for the real number k belongs to B, there is no original image in a, find K Come on, see who can write it
• 4. High school mathematics problem: determine that the equation (X-2) (X-5) = 1 has two different real number solutions, and one is greater than 5, one is less than 2
• 5. If a √ a + B √ B ＞ a √ B + B √ a, then the condition that real numbers a and B should satisfy is? If a √ a + B √ B ＞ a √ B + B √ a, then the condition that real numbers a and B should satisfy is?
• 6. Let a = {the square of X / x-3x + 2 = 0}, B = {the square of X / x + 2 (a + 1) x + (the square of a-5) = 0. If AUB = a, find the value range of real number a? Complete solution steps, at least I can understand! The answer is given, where △ is the square of 4 (a + 1) - 4 (the square of a - 5) = 8 (a + 3); how did it come from? Why do we have to use it to judge? This △ = 4 (a + 1) square-4 (A's square-5) = 8 (a + 3); how can we get it? Or is there a dead formula for such a similar problem, as long as it's hard? Sorry, it's a bit stupid @!
• 7. x. Y is a real number P: X ＞ Y Q: | x | y|
• 8. In the set of real numbers a, - A, | a |, the elements are
• 9. X y is a real number and X & # 178; - 2x + √ XY-2 = - 1, find the value of 1 / XY + 1 / (x + 1) (y + 1) +. + 1 / (x + 2006) (y + 2006) Sorry for the inconvenience
• 10. All the solutions of the equation y = x & # 178; + 1
• 11. Let a = {(x, y) | y = 2x-1, X ∈ n *}, B = {(x, y) | y = AX2 ax + A, X ∈ n *}, ask whether there is a non-zero integer a, so that a ∩ B ≠? If it exists, request the value of a; if it does not exist, explain the reason
• 12. Let a = {(x, y) | y = 2x-1, X ∈ positive natural number}, B = {(x, y) | y = ax ^ 2-ax + A, X ∈ positive natural number}, ask whether there is a non-zero real number a, let a ∩ B be If there is a single element set, find out the value of A. if not, explain the reason
• 13. Proof: the equation AX ^ 2 + 2x + 1 = 0 of X has at least one negative root if and only if a
• 14. p: For any real number x, KX square plus 2, KX minus (k plus 2) is less than 0. Q: for the equation x of X, the square plus x minus K is equal to 0, and there is a real root if P and Q p: For any real number x, KX square plus 2, KX minus (k plus 2) is less than 0. Q: for the equation x of X, the square plus x minus K is equal to 0. There is a real root. If there is only one true proposition between P and Q, the value range of the real number k is determined
• 15. The real solution of the equation (2 + I) x square minus (5 + I) x plus (2 minus 2I) = 0 is
• 16. The equation | x ^ 2 + ax + B | = 2 of X has three different real numbers, and the three different real numbers are exactly three sides of a right triangle. Find the right triangle
• 17. F (x) = ax + BX + 1 (a, B ∈ R) if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression of F (x) is obtained F (x) = ax + BX + 1 (a, B ∈ R) ① if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression for finding f (x) holds. ② under the condition of ①, when x ∈ [- 2,2], G (x) = f (x) - KX is a monotone increasing function, the value range of real number k can be found
• 18. If the real numbers a and B satisfy A2 + B2 ≤ 1, then the probability of the equation x2-ax + 34b2 = 0 with real roots is zero______ ．
• 19. If the real numbers a and B satisfy A2 + B2 ≤ 1, then the probability of the equation x2-ax + 34b2 = 0 with real roots is zero______ ．
• 20. In the interval [- 1,1], take any two points a and B, and the probability that the two points of equation x2 + ax + B = 0 are both real numbers is p, then the value range of P is___ ．