Multiple choice

If 0< a < b < c, and the roots $\alpha ,\beta $ of the equation ${ ax }^{ 2 }+bx+c=0$ are complex numbers, then _______________.

  1. ${ |\alpha |=|\beta | }$
  2. ${ |\alpha |>1 }$
  3. ${ |\beta | }<1 $

  4. None of these
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A Correct answer
AI explanation

Since the given coefficients a, b, and c are real numbers, the complex roots alpha and beta must be complex conjugates of each other. Complex conjugates always have the same magnitude because their real parts are identical and their imaginary parts are equal in absolute value. Therefore, the absolute values of the two roots are equal, making the magnitude of alpha equal to the magnitude of beta.

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