JEE Main 2023 — Quadratic Equation Questions with Solutions

If the value of real number α > 0 for which x 2 - 5 α x + 1 = 0 and x 2 - α x - 5 = 0 have a common…

The number of real roots of the equation x x - 5 x + 2 + 6 = 0 , is

Let α ,   β be the roots of the equation x 2 - 2 x + 2 = 0 Then α 14 + β 14 is equal to

Let S = x : x ∈ ℝ  and  3 + 2 x 2 - 4 + 3 - 2 x 2 - 4 = 10 . Then n S is equal to

Let m and n be the numbers of real roots of the quadratic equations x 2 - 12 x + [ x ] + 31 = 0 and x 2 - 5 | x + 2 | -…

Let α ,   β ,   γ be the three roots of the equation x 3 + b x + c = 0 if β γ = 1 =…

The number of real roots of the equation x 2 - 4 x + 3 + x 2 - 9 = 4 x 2 - 14 x + 6 , is:

The number of integral values of k , for which one root of the equation 2 x 2 - 8 x + k = 0 lies in the interval 1 , 2…

Let λ ∈ ℝ and let the equation E be | x | 2 - 2 | x | + | λ - 3 | = 0 . Then the largest element…

If a and b are the roots of the equation x 2 - 7 x - 1 = 0 , then the value of a 21 + b 21 + a 17 + b 17 a 19 + b 19 is…