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Black Book Advanced Problems in MathematicsMathematicsQuadratic Equation

If a, b, c are rational numbers ( a > b > c > 0 ) and quadratic equation (a+b-2c)x^2 + (b+c-2a)x + (c+a-2b) = 0 has a root in the interval (-1, 0) then which of the following statement(s) is/are correct?

Options

  1. Aa + c < 2b
  2. Bboth roots are rational
  3. Cax^2 + 2bx + c = 0 have both roots negative
  4. Dcx^2 + 2bx + a = 0 have both roots negative.

Correct answer

A. a + c < 2b

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