Multiple choice

If the quadratic equations $3x^{2} + ax + 1 = 0$ and $2x^{2} + bx + 1 = 0$ have a common root, then the variable point $(a, b)$ moves on

  1. A circle

  2. A parabola

  3. An ellipse

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

If alpha is the common root, 3alpha^2 + a*alpha + 1 = 0 and 2alpha^2 + b*alpha + 1 = 0. Subtracting: alpha^2 + (a-b)alpha = 0. So alpha = 0 (impossible as 1=0) or alpha = b-a. Substituting alpha = b-a into the first: 3(b-a)^2 + a(b-a) + 1 = 0. This is a quadratic in a and b representing a hyperbola.

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