Multiple choice

Find the value of p if the equation $3x^2-2x+p=0$ and $6x^2-17x+12=0$ have a common root.

  1. $-8/3,-15/4$
  2. $-7/3,-14/3$
  3. $2,4$

  4. none of these 
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A Correct answer
Explanation

Solve 6x^2 - 17x + 12 = 0 using the quadratic formula or factoring: (2x-3)(3x-4)=0, so roots are 3/2 and 4/3. Substitute these into 3x^2 - 2x + p = 0. For x=3/2: 3(9/4) - 2(3/2) + p = 0 => 27/4 - 3 + p = 0 => p = -15/4. For x=4/3: 3(16/9) - 2(4/3) + p = 0 => 16/3 - 8/3 + p = 0 => p = -8/3.

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