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Black Book Advanced Problems in MathematicsMathematicsQuadratic Equation

The quadratic polynomials defined on real coefficients P(x) = a₁x^2 + 2b₁x + c₁, Q(x) = a₂x^2 + 2b₂x + c₂, P(x) and Q(x) both take positive values x R . If f(x) = a₁a₂x^2 + b₁b₂x + c₁c₂ , then:

Options

  1. Af(x) < 0 x R
  2. Bf(x) > 0 x R
  3. Cf(x) takes both positive and negative values
  4. DNothing can be said about f(x) .

Correct answer

B. f(x) > 0 x R

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