MathDB

4

Part of 2000 National High School Mathematics League

Problems(1)

A Lot of Numbers

Source: 2000 National High School Mathematics League, Exam One, Problem 4

3/10/2020
Give positive numbers p,q,a,b,cp,q,a,b,c, if p,a,qp,a,q is a geometric series, p,b,c,qp,b,c,q is an arithmetic sequence. Then, wich is true about the equation bx2āˆ’ax+c=0bx^2-ax+c=0? (A)\text{(A)} It has no real roots. (B)\text{(B)} It has two equal real roots. (C)\text{(C)} It has two different real roots, and their product is positive. (D)\text{(D)} It has two different real roots, and their product is negative.
geometric seriesarithmetic sequence