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MHT CET20239 May 2023Evening ShiftMathematicsQuadratic EquationActual

In ABC , with tustal notations, m C = 2 , if ( A 2 ) and ( B 2 ) are the roots of the equation. a ₁ x^2+ b ₁ x+ c ₁=0 ( a ₁ 0 ) , then

Options

  1. Aa₁+b₁=c₁
  2. Bb₁+c₁=a₁
  3. Ca ₁+ c ₁- b ₁
  4. Db₁=c₁

Correct answer

A. a₁+b₁=c₁

Step-by-step solution

array ll & In ABC , & A + B + C =180^ & A + 2 + B =180^ & A + B = 2 & A 2 + B 2 = 4 array ( A 2 ) and ( B 2 ) are roots of equation a ₁ x^2+ b ₁ x+ c ₁=0 ... [Given] aligned & Sum of roots = -b₁ a₁ & ( A 2 )+ ( B 2 )= -b₁ a₁ aligned Also, ( A 2 ) ( B 2 )= c ₁ a ₁ Using ( A 2 + B 2 )= A 2 + B 2 1- A 2 B 2 , we get aligned & ( 4 )= -b₁ a₁ 1- c₁ a₁ & 1= -b₁ a₁-c₁ & a₁-c₁=-b₁ & a₁+b₁=c₁ aligned

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