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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

Let f(x) = x^2 + ax + b and g(x) = x^2 + cx + d be two quadratic...

Let f(x)=x2+ax+bf(x) = x^2 + ax + b and g(x)=x2+cx+dg(x) = x^2 + cx + d be two quadratic polynomials with real coefficients and satisfy ac=2(b+d)ac = 2(b + d). Then which of the following is (are) correct?

Options

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

Correct answer

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

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