Multiple choice

If $a$ and $b$ are the roots of the equation $y=\dfrac{1}{3}x^2-2x+3$, then find $|a-b|$.

  1. $0$
  2. $1$
  3. $2$
  4. $3$
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A Correct answer
Explanation

The roots a and b are solutions to (1/3)x^2 - 2x + 3 = 0, which is x^2 - 6x + 9 = 0. This factors to (x-3)^2 = 0, so a = 3 and b = 3. Thus, |a-b| = |3-3| = 0.

AI explanation

The discriminant of the quadratic equation determines the nature of its roots, calculated using b^2 - 4ac. For the equation (1/3)x^2 - 2x + 3 = 0, the discriminant is (-2)^2 - 4(1/3)(3), which equals 4 - 4 = 0. A zero discriminant means both roots are real and equal, so their absolute difference is 0.

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