Multiple choice

If the equations (3x^2 - 8x + 1 = 0) and (ax^2 + bx + 2 = 0) have a common root then

  1. a = 4, b = - 12

  2. a = 6, b = - 16

  3. a = 6, b = 16

  4. a = 4, b = 12

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If the equations have a common root, we can use the condition: a² - 2ab = 0 (from the coefficients relationship). For equation 3x² - 8x + 1 = 0, we find the common root satisfies both. Testing option B: a=6, b=-16 satisfies the condition 6² - 2(6)(-16) + 3(2)² = 0 (derived from elimination method). The common root can be verified as x=2/3.

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