Let be real numbers

MATHEMATICS · Single correct · CBSE · Mathematics · Polynomials · Polynomials

Problem

Let a,b,c,p,qa,b,c,p,q be real numbers. Suppose α,β\alpha,\beta are roots of x2+2px+q=0x^2+2px+q=0 and α,1β\alpha,\frac{1}{\beta} are roots of ax2+2bx+c=0ax^2+2bx+c=0, where β2∉{−1,0,1}\beta^2\notin\{-1,0,1\}. Statement 1: (p2−q)(b2−ac)≥0(p^2-q)(b^2-ac)\geq0. Statement 2: b≠pab\ne pa or c≠qac\ne qa. (1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1 (2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 (3) Statement 1 is true, Statement 2 is false (4) Statement 1 is false, Statement 2 is true

Related theory

Browse the problem library