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MHT CET202519 Apr 2025Evening ShiftMathematicsQuadratic EquationActual

If triangle A B C is a right angled at A and B 2 , C 2 are roots of the equation a x^2+b x+c=0, a 0 , then

Options

  1. Aa+c=b
  2. Ba+b=c
  3. Cb + c =a
  4. Da+c=2 b

Correct answer

B. a+b=c

Step-by-step solution

The quadratic equation ax^2 + bx + c = 0 has roots B 2 and C 2 , giving the root relationships: B 2 + C 2 = - b a B 2 C 2 = c a For a right triangle with angle A = 90^ , the angle sum B + C = 90^ implies B+C 2 = 45^ . Applying the tangent sum identity: B 2 + C 2 1 - B 2 C 2 = 45^ = 1 Substituting the root relationships: - b a 1 - c a = 1 Simplifying yields -b = a - c , or equivalently a + b = c . This corresponds to option B .

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