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COMEDK2018MathematicsQuadratic Equation

If , , are the roots of the equation x³+p x+q=0 , then the value of the determinant | array ccc & & & & & & array | is

Options

  1. Aq
  2. B0
  3. Cp
  4. Dp²-2 q

Correct answer

B. 0

Step-by-step solution

We have, , and are roots of equation gathered x³+p x+q=0 + + =0 Here, + + =p =-q Applying C₁ C₁+C₂+C₃ , we get | array lll + + & & + + & & + + & & array |=( + + ) | array ccc 1 & & 1 & & 1 & & array | gathered Applying R₂ R₂-R₁, R₃ R₃-R₁ , we get aligned &( + + ) | array ccc 1 & & 0 & - & - 0 & - & - array | &=( + + )[( - )( - )-( - )( - )] &=0 [( - )( - )-( - )( - )]=0 aligned

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