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Manipal MET2012MathematicsQuadratic Equation

If f(x)=x^2+2 b x+2 c^2 and g(x)=-x^2-2 c x+b^2 are such that f(x) g(x) , then relation between b and c is

Options

  1. Ano relation
  2. B0 c b 2
  3. C|c| 2 |b|
  4. D|c| 2 |b|

Correct answer

D. |c| 2 |b|

Step-by-step solution

aligned We have, f(x)=(x+b)^2+2 c^2-b^2 f(x)=2 c^2-b^2 and g(x)=b^2+c^2-(x+c)^2 g(x)=b^2+c^2 Thus, f(x) g(x) 2 c^2-b^2 b^2+c^2 c^2 2 b^2 |c| 2 |b| aligned

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