JEE Main 2021 — Quadratic Equation Questions with Solutions

The integer k , for which the inequality x 2 - 2 3 k - 1 x + 8 k 2 - 7 > 0 is valid for every x in R is:

The probability of selecting integers a ∈ - 5 , 30 such that x 2 + 2   a + 4   x - 5 a + 64 > 0 , f…

The number of real roots of the equation e 4 x - e 3 x - 4 e 2 x - e x + 1 = 0 is equal to

Let α and β be two real numbers such that α + β = 1 and α β = - 1 . Let p n = α n +…

Let α , β be two roots of the equation x 2 + 20 1 / 4 x + 5 1 / 2 = 0 . Then α 8 + β 8 is equal to

If α , β ∈ R are such that 1 - 2 i (here i 2 = - 1 ) is a root of z 2 + α z + β = 0 , then &#…

The number of the real roots of the equation x + 1 2 + | x - 5 | = 27 4 is ________.

The number of pairs a , b of real numbers, such that whenever α is a root of the equation x 2 + a x + b = 0 , &#16…

Let p and q be two positive numbers such that p + q = 2 and p 4 + q 4 = 272 . Then p and q are roots of the equation:

The set of all values of k > - 1 , for which the equation 3 x 2 + 4 x + 3 2 - ( k + 1 ) 3 x 2 + 4 x + 3 3 x 2 + 4 x…