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Quadratic Inequality

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsWhat condition on \(a\) is necessary for the equation \(3x^2-2(2a+1)x+(a^2+a+1)=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsLet U = ℝ, A = {x ∈ ℝ : (x - 2)(x + 5) ≤ 0}, and B = {x ∈ ℝ : |x - 1| < 3}. What is (A′ ∩ B)′?Class 10SetsComplement of a Set and Its PropertiesLevel 21Hard MathematicsIf U = R and A = {x ∈ R : x² + 2x − 8 < 0}, what is A′?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf U = {x : x ∈ ℤ, −12 ≤ x ≤ 12} and A = {x : x ∈ U, x² − 9x + 18 ≤ 0}, what is n(A′)?Class 10SetsComplement of a Set and Its PropertiesLevel 21Hard MathematicsLet U = {x ∈ ℤ | −4 ≤ x ≤ 6} and A = {x ∈ U | (x − 1)(x + 2) ≥ 0}. What is A′, the complement of A with respect to U?Class 10SetsComplement of a Set and Its PropertiesLevel 10Hard MathematicsIf the universal set is U = ℝ and A = {x ∈ ℝ : x² − 6x + 8 > 0}, what is A′?Class 10SetsComplement of a Set and Its PropertiesLevel 20Medium MathematicsIf U = {x : x ∈ Z, -8 ≤ x ≤ 8} and A = {x : x ∈ U, x² - 2x - 15 ≤ 0}, how many elements are in A′?Class 10SetsComplement of a Set and Its PropertiesLevel 19Medium MathematicsIf U = {x ∈ ℤ | −5 ≤ x ≤ 5} and A = {x ∈ U | x² < 10}, find A′, the complement of A with respect to U.Class 10SetsComplement of a Set and Its PropertiesLevel 19Medium MathematicsIf U = R and A = {x ∈ R : x² + x − 6 ≥ 0}, what is A'?Class 10SetsComplement of a Set and Its PropertiesLevel 21Hard MathematicsIf U = R and A = {x : x² − 4x − 12 < 0}, what is A'?Class 10SetsComplement of a Set and Its PropertiesLevel 21Medium MathematicsIf U = {x : x ∈ ℤ, −10 ≤ x ≤ 10} and A = {x : x² − 9x + 20 ≤ 0}, what is A′?Class 10SetsComplement of a Set and Its PropertiesLevel 20Hard MathematicsIf U = ℝ and A = {x : x² − 2x − 8 ≤ 0}, what is A'?Class 10SetsComplement of a Set and Its PropertiesLevel 10Hard MathematicsIf U = R and A = {x ∈ R : x² − 9 > 0}, what is A′?Class 10SetsComplement of a Set and Its PropertiesLevel 20Hard MathematicsIf \(U=\{x:x\in\mathbb{Z},-8\le x\le8\}\) and \(A=\{x:x^2-4x\le0\}\), what is \(A'\)?Class 10SetsComplement of a Set and Its PropertiesLevel 20Hard MathematicsIf the universal set is \(U=\mathbb{R}\) and \(A=\{x:x^2-1\ge 0\}\), what is \(A'\)?Class 10SetsComplement of a Set and Its PropertiesLevel 19Medium MathematicsIf \(U=\mathbb{R}\) and \(A=\{x:x^2<16\}\), what is \(A'\)?Class 10SetsComplement of a Set and Its PropertiesLevel 19Medium MathematicsIf U = {x : x ∈ ℤ, −5 ≤ x ≤ 5} and A = {x : x² ≤ 9}, what is A'?Class 10SetsComplement of a Set and Its PropertiesLevel 19Easy MathematicsIf the universal set \(U=\{x\in\mathbb Z\mid -5\le x\le 5\}\) and \(A=\{x\in\mathbb Z\mid x^2<9\}\), what is the complement \(A^c\) of A?Class 10SetsComplement of a Set and Its PropertiesLevel 20Medium MathematicsLet U = {x : x ∈ ℤ, -4 ≤ x ≤ 4} and A = {x : x² ≤ 4}. What is the complement Aᶜ of A with respect to U?Class 10SetsComplement of a Set and Its PropertiesLevel 19Medium MathematicsIf A = {x ∈ R : 0 ≤ x ≤ 4} and B = {x ∈ R : x² − 4x + 3 ≤ 0}, what is A ∩ B?Class 10SetsOperations on Sets (Union, Intersection, Difference)Level 16Medium