Multiple choice

Let $a,b,c$ be positive real numbers. The number of real roots the equation $(a{x}^{2}+bx-c)(b{x}^{2}+cx-a)(c{x}^{2}+ax-b)=0$ may have, is

  1. 2

  2. 0

  3. 4

  4. 6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Each quadratic factor (ax^2 + bx - c), (bx^2 + cx - a), and (cx^2 + ax - b) has a discriminant D = b^2 - 4ac. For the first: D1 = b^2 + 4ac. Since a, b, c > 0, D1 > 0, so it has 2 real roots. Similarly, D2 = c^2 + 4ab > 0 and D3 = a^2 + 4bc > 0. Each factor provides 2 distinct real roots, totaling 6.

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