Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If, for a positive integer n, the quadratic equation, x(x + 1) + (x + 1)(x + 2) + + (x + n - 1 )(x + n) = 10n has two consecutive...
- Let S = x R : x 0 and 2| x - 3| + x ( x - 6) + 6 = 0 . Then S :
- Let p, q and r be real numbers (p q, r 0), such that the roots of the equation 1 x+p + 1 x+q = 1 r are equal in magnitude but...
- If an angle A of a satisfies 5 A + 3 = 0, then the roots of the quadratic equation, 9x^2 + 27x + 20 = 0 are -
- The sum of the solutions of the equation | x - 2| + x ( x - 4) + 2 = 0, (x > 0) is equal to:
- If three distinct numbers a, b, c are in G.P. and the equations ax^2 + 2bx + c = 0 and dx^2 + 2ex + f = 0 have a common root,...
- The number of integral values of m for which the equation (1 + m^2)x^2 - 2(1 + 3m)x + (1 + 8m) = 0 has no real root is:
- Let p, q ∈ R. If 2 - 3 is a root of the quadratic equation, x^2 + px + q = 0, then:
- If R is such that the sum of the cubes of the roots of the equation, x^2 + (2 - )x + (10 - ) = 0 is minimum, then the magnitude...
- If tan A and tan B are the roots of the quadratic equation, 3x^2 - 10x - 25 = 0 then the value of 3 ^2(A + B) - 10 (A + B) (A +...
- If f(x) is a quadratic expression such that f(1) + f(2) = 0, and –1 is a root of f(x) = 0, then the other root of f(x) = 0 is -
- If m is chosen in the quadratic equation (m^2 + 1)x^2 - 3x + (m^2 + 1)^2 = 0 such that the sum of its roots is greatest, then the...
- If α and β are the roots of the quadratic equation, x^2 + x - 2 = 0, (0, 2 ), then ^ 12 + ^ 12 ( ^ -12 + ^ -12 ) ( - )^ 24 is...
- The number of all possible positive integral values of α for which the roots of the quadratic equation, 6x^2 - 11x + = 0 are...
- If both the roots of the quadratic equation x^2 - mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m...
- The number of integral values of m for which the quadratic expression, (1 + 2m)x^2 - 2(1 + 3m)x + 4(1 + m), x ∈ R, is always...
- If λ be the ratio of the roots of the quadratic equation in x, 3m^2x^2 + m(m - 4)x + 2 = 0, then the least value of m for which +...
- All x satisfying the inequality ( ^ -1 x)^2 - 7( ^ -1 x) + 10 > 0, lie in the interval:
- If one real root of the quadratic equation 81x^2 + kx + 256 = 0 is cube of the other root, then a value of k is:
- The value of λ such that sum of the squares of the roots of the quadratic equation, x^2 + (3 - )x + 2 = has the least value is:
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration