Multiple choice

If $1$ is a root of the equations $ay^2 + ay + 3 = 0$ and $y^2 + y + b = 0$, then $ab$ equals:

  1. $3$
  2. $-\dfrac{7}{2}$
  3. $6$
  4. $-3$
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A Correct answer
Explanation

If 1 is a root, then a(1)^2 + a(1) + 3 = 0, so 2a = -3, a = -1.5. Also, 1^2 + 1 + b = 0, so 2 + b = 0, b = -2. Then ab = (-1.5) * (-2) = 3.

AI explanation

Since y = 1 is a root of both equations, substituting 1 for y gives a(1)^2 + a(1) + 3 = 0, which simplifies to 2a + 3 = 0 and a = -3/2. Substituting 1 for y in the second equation gives (1)^2 + 1 + b = 0, so b = -2. Multiplying these values gives ab = (-3/2) * (-2) = 3.

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