Quadratic Equation: Challenging Problems for JEE Mains and Advanced скачать в хорошем качестве

Quadratic Equation: Challenging Problems for JEE Mains and Advanced

In this LIVE session, we are challenging problems for JEE Mains and Advanced challenging problem series Problems Discussed: Quadratic Equation Problem 1. Complete set of real values of ’ a ’ for which the equation x4 − 2ax2 + x + a2 − a = 0 has all its roots real : (A) 3 4 ,∞ (B) [1,∞) (C) [2,∞) (D) [0,∞) Problem 2. The number of integral roots of the equation x8 − 24x7 − 18x5 +39x2 +1155 = 0 is: (A) 0 (B) 2 (C) 4 (D) 6 Problem 3. Let a,b,c be the lengths of the sides of a triangle (no two of them are equal) and k ∈ R. If the roots of the equation x2 + 2(a + b+c)x+6k(ab+bc+ca) are real, then 4 Problem 4. Find all the real values of ’ a ’ for which the equation x4 + (a − 1)x3 + x2 + (a − 1)x + 1 = 0 possesses at least two distinct negative roots. Problem 5. Let x,y be positive integers satisfying y2−xy−x2 = 1. Solve for x and y. Also find the limiting value of y x as x → ∞. 1 HWProblem. HW1.(Multi Correct Option) If α,β are the roots of equation (k + 1)x2 − (20k + 14)x + 91k + 40 = 0;(α β),k 0 then which of the following is/are correct? (A) the larger root (β) lie in the interval: (4,7) (B) the larger root (β) lie in the interval: (10,13) (C) the smaller root (α) lie in the interval: (4,7) (D) the smaller root (α) lie in the interval: (7,10) HW2.(Similar to JEE Advanced 2017) Let p,q be integers and let α,β be the roots of the equation, x2 −x−1 = 0 where α̸ = β. For n =0,1,2,......... let an = pαn +qβn. If a4 = 28, then Find the value of p and q in lowest terms. Find p + q jee challenging questions jee advanced level problems jee mains tough questions hard maths problems for jee jee problem solving series advanced problem solving maths jee high level questions iit jee tough problems concept based jee questions jee mains 2026 January attempt solutions jee mains 2026 paper jee mains 2026 live jee mains 2026 january attempt jee mains 2026 jee 2026 jee mains preparation jee mains maths jee mains physics jee mains chemistry jee aspirants 2026 jee strategy 2026 jee mains tips jee mains motivation jee mains exam jee mains syllabus jee mains important questions jee mains revision jee mains mock test jee mains analysis jee mains expected questions jee mains rank boost