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MHT CET202411 May 2024Evening ShiftMathematicsQuadratic EquationActual

In a PQR , m R = 2 . If ( P 2 ) and ( Q 2 ) are the roots of the equation a x^2+b x+c=0(a 0) , then

Options

  1. Aa + b = c
  2. Bb + c = a
  3. Ca + c = b
  4. Db = c

Correct answer

A. a + b = c

Step-by-step solution

aligned & In PQR & P + Q + R =180^ & P + Q + 2 =180^ & P + Q = 2 & P 2 + Q 2 = 4 aligned ( P 2 ) and ( Q 2 ) are roots of the equation a x^2+b x+c=0 ...[Given] Sum of roots = -b a ( P 2 )+ ( Q 2 )= - b a Also, ( P 2 ) ( Q 2 )= c a Using, ( P 2 + Q 2 )= P 2 + Q 2 1- P 2 Q 2 , we get aligned & ( 4 )= -b a 1- c a & 1= -b a-c & a - c =- b & a + b = c aligned

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