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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Quadratic Equation

Black Advanced Problems in Mathematics · Mathematics · Quadratic Equation

If a, b, c are rational numbers ( a > b > c > 0 ) and quadratic...

If a,b,ca, b, c are rational numbers (a>b>c>0a > b > c > 0) and quadratic equation (a+b−2c)x2+(b+c−2a)x+(c+a−2b)=0(a+b-2c)x^2 + (b+c-2a)x + (c+a-2b) = 0 has a root in the interval (−1,0)(-1, 0) then which of the following statement(s) is/are correct?

Options

  1. Aa+c<2ba + c < 2b
  2. Bboth roots are rational
  3. Cax2+2bx+c=0ax^2 + 2bx + c = 0 have both roots negative
  4. Dcx2+2bx+a=0cx^2 + 2bx + a = 0 have both roots negative.

Correct answer

A. a+c<2ba + c < 2b

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