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COMEDK2014MathematicsDeterminants

If , , are the roots of x³+a² x+b=0 , then the value of | array lll & & & & & & array | is

Options

  1. A-a³
  2. Ba³-3 b
  3. Ca³
  4. D0

Correct answer

D. 0

Step-by-step solution

Given, equation is x³+a² x+b=0 Since, , , are its roots. Sum of roots = + + =0 ...(i) Now, | array lll & & & & & & array | Using operation C₁ C₁+C₂+C₃ , we get | array lll ( + + ) & & ( + + ) & & ( + + ) & & array |= | array lll 0 & & 0 & & 0 & & array |=0 [Using Eq. (i)]

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