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Black Book Advanced Problems in MathematicsMathematicsQuadratic Equation

Let f(x) = x^2 + ax + b and g(x) = x^2 + cx + d be two quadratic polynomials with real coefficients and satisfy ac = 2(b + d) . Then which of the following is (are) correct?

Options

  1. AExactly one of either f(x) = 0 or g(x) = 0 must have real roots.
  2. BAtleast one of either f(x) = 0 or g(x) = 0 must have real roots.
  3. CBoth f(x) = 0 and g(x) = 0 must have real roots.
  4. DBoth f(x) = 0 and g(x) = 0 must have imaginary roots.

Correct answer

B. Atleast one of either f(x) = 0 or g(x) = 0 must have real roots.

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