JEE Main 2022 — Quadratic Equation Questions with Solutions

If for some p , q , r ∈ R , all have positive sign, one of the roots of the equation p 2 + q 2 x 2 - 2 q p + r x…

The sum of all real values of x for which 3 x 2 - 9 x + 17 x 2 + 3 x + 10 = 5 x 2 - 7 x + 19 3 x 2 + 5 x + 12 is equal…

The number of real solutions of the equation e 4 x + 4 e 3 x - 58 e 2 x + 4 e x + 1 = 0 is _____.

Let a , b ∈ R be such that the equation a x 2 - 2 b x + 15 = 0 has repeated root α and if α and β…

Let α , β be the roots of the equation x 2 - 2 x + 6 = 0 and 1 α 2 + 1 , 1 β 2 + 1 be the roots of…

If the sum of the squares of the reciprocals of the roots α and β of the equation 3 x 2 + λ x - 1 = 0 is…

The sum of all real roots of equation e 2 x - 4 6 e 2 x - 5 e x + 1 = 0 is

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 t…

The minimum value of the sum of the squares of the roots of x 2 + 3 - a x = 2 a - 1 is

The sum of the cubes of all the roots of the equation x 4 - 3 x 3 - 2 x 2 + 3 x + 1 = 0 is _____.