JEE Main 2024 — Quadratic Equation Questions with Solutions

Let α, β be roots of x²+√(2) x-8=0. If Un=αⁿ+βⁿ, then U₁₀+√(2) U₉2 U₈ is equal to______

Let x₁, x₂, x₃, x₄ be the solution of the equation 4 x⁴+8 x³-17 x²-12 x+9=0 and (4+x₁² ) (4+x₂² ) (4+x₃² ) (4+x₄² )=(12…

If 2 and 6 are the roots of the equation a x²+b x+1=0, then the quadratic equation, whose roots are (1)/(2 a+b) and (1)…

Let α, β be the distinct roots of the equation x²- (t²-5 t+6 ) x+1=0, t R and an=αⁿ+βⁿ. Then the minimum value of a₂₀₂₃…

The number of real solutions of the equation x|x+5|+2|x+7|-2=0 is_________

The number of distinct real roots of the equation |x+1||x+3|-4|x+2|+5=0, is

Let S be the set of positive integral values of a for which a x 2 + 2 a + 1 x + 9 a + 4 x 2 - 8 x + 32 < 0 , ∀ x ∈ ℝ .…

The number of real solutions of the equation x (x²+3|x|+5|x-1|+6|x-2| )=0 is ______.

Let α, β be roots of equation x²-70 x+λ=0 , where (λ)/(2), (λ)/(3) . If λ assumes the minimum possible value, then (√(α…

The number of solutions, of the equation e sin x − 2 e − sin x = 2 is