Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- The number of real solutions of the equation, x^2-|x|-12=0 is
- Let , be two roots of the equation x^2+(20)^ 1/4 x+(5)^ 1/2 =0. Then ^8+ ^8 is equal to
- The set of all values of k>-1, for which the equation (3x^2+4x+3 )^2-(k+1) (3x^2+4x+3 ) (3x^2+4x+2 )+k (3x^2+4x+2 )^2=0 has real...
- The number of pairs (a,b) of real numbers, such that whenever is a root of the equation x^2+ax+b=0, ^2-2 is also a root of this...
- If and are the roots of the quadratic equation, x^2+x -2 =0, (0, 2 ), then ^ 12 + ^ 12 ( ^ -12 + ^ -12 ) ( - )^ 24 is equal to
- If , are the roots of the equation x^2- (5+3^ _35 -5^ _53 )x+3 (3^ _35 -5^ _53 -1 )=0, then the equation, whose roots are + 1 and...
- Let , be the roots of the equation x^2- 2x+ 6=0 and 1 ^2 +1, 1 ^2 +1 be the roots of the equation x^2+ax+b=0. Then the roots of...
- Let f(x)=ax^2+bx+c be such that f(1)=3, f(-2)= and f(3)=4. If f(0)+f(1)+f(-2)+f(3)=14, then is equal to
- If the sum of the squares of the reciprocals of the roots and of the equation 3x^2+ x-1=0 is 15, then 6 ( ^3+ ^3 )^2 is equal to
- Let a,b R be such that the equation ax^2-2bx+15=0 has a repeated root . If and are the roots of the equation x^2-2bx+21=0, then...
- Let f(x) be a quadratic polynomial such that f(-2)+f(3)=0. If one of the roots of f(x)=0 is -1, then the sum of the roots of...
- The minimum value of the sum of the squares of the roots of x^2+(3-a)x+1=2a is
- Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0)=p, p 0, and f(1)= 13. If the equations f(x)=0 and f...
- Let m and n be the numbers of real roots of the quadratic equations x^2-12x+[x]+31=0 and x^2-5|x+2|-4=0 respectively, where [x]...
- The number of elements in the set n Z: |n^2-10n+19 |<6 is
- The least positive value of a for which the equation, (the equation is not legible in the source), has real roots is
- If x=-1,-4 are roots of the equation x=-1 and C-3:x - ,-2) for each positive integer -x^2+5x+16=0, then the value of x^2-5x-16=0...
- The sum of all integral values of k (k 0) for which the equation 2 x-1 - 1 x-2 = 2k in x has no real roots, is
- If for some p,q,r R, not all have same sign, one of the roots of the equation (p^2+q^2 )x^2-2q(p+r)x+q^2+r^2=0 is also a root of...
- Let a,b (a>b) be the roots of the quadratic equation x^2-x-4=0. If P_n= ^n- ^n, n N, then P_ 15 P_ 16 -P_ 14 P_ 16 -P_ 15 ^2+P_...
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