Multiple choice

If $'2'$ is repeated root of the cubic equation $3{x}^{3}+p{x}^{2}+qx-12=0$ Then the value of $p+q$ is

  1. $9$
  2. $27$
  3. $3$
  4. $N.O.T$
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A Correct answer
Explanation

If 2 is a repeated root, f(2) = 0 and f'(2) = 0. f(x) = 3x^3 + px^2 + qx - 12. f'(x) = 9x^2 + 2px + q. f'(2) = 36 + 4p + q = 0 => 4p + q = -36. f(2) = 24 + 4p + 2q - 12 = 0 => 4p + 2q = -12. Subtracting: q = 24. Then 4p + 24 = -36 => 4p = -60 => p = -15. p + q = -15 + 24 = 9.

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