For how many ordered triples of positive real numbers (a,b,c), do the equations ax^2+2bx+c, bx^2+2cx+a and cx^2+2ax+b each have 2 distinct real roots?

1 answer

we want the discriminants to be positive. So,

b^2 - 4ac > 0
c^2 - 4ab > 0
a^2 - 4bc > 0

After playing around with this for a while, I was still stumped, so I went to wolframalpha.com, and it said that there were no all-positive solutions.

??
Similar Questions
    1. answers icon 0 answers
  1. a, b, c, A and C are real numbers that satisfy the equation(ax^2+bx+c)^2=Ax^4+16x^3+28x^2+24x+C How many possible ordered
    1. answers icon 1 answer
  2. a, b, c, A and C are real numbers that satisfy the equation(ax2+bx+c)2=Ax4+16x3+28x2+24x+C How many possible ordered triples of
    1. answers icon 0 answers
  3. An ordered triple of real numbers(a,b,c) is called friendly, if each number is equal to the product of the other 2. How many
    1. answers icon 0 answers
more similar questions