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Manipal MET2010MathematicsQuadratic Equation

If a 1 , roots of the equation (1-a) x^2+3 a x-1=0 are

Options

  1. Aone positive and one negative
  2. Bboth negative
  3. Cboth positive
  4. Dboth non-real complex

Correct answer

C. both positive

Step-by-step solution

Let , are the roots of the equation (1-a) x^2+3 a x-1=0 , then + = 3 a a-1 , = 1 a-1 As a 1, + 0 and 0 and D=9 a^2+4(1-a)=9 (a^2- 4 9 a+ 4 9 )=9 a (a- 4 9 )+ 4 9 0 , as a 1 The equation has real and positive roots.

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