Common Roots

JEE Main Mathematics · Quadratic Equations · 4 questions, latest first

• Let a be the sum of all coefficients in the expansion of (1-2 x+2 x^2)^2023(3-4 x^2+2 x^3)^2024 and b= lim_x → 0((∫_0^x (log…202431 January, Shift 1 · Q7
• The parabolas: a x^2+2 b x+c y=0 and d x^2+2 e x+f y=0 intersect on the line y=1. If a, b, c, d, e, f are positive real numbers…202330 January, Shift 2 · Q72
• If the value of real number a>0 for which x^2-5 a x+1=0 and x^2-a x-5=0 have a common real root is 3/(√(2 β)) then β is equal to…202330 January, Shift 2 · Q82
• Let λ ≠ 0 be a real number. Let α, β be the roots of the equation 14 x^2-31 x+3 λ=0 and α, γ be the roots of the equation 35…202329 January, Shift 1 · Q64