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MHT CET20249 May 2024Evening ShiftMathematicsQuadratic EquationActual

Let , be the roots of the equation x^2-p x+r=0 and 2 , 2 be the roots of the equation x^2- q x+ r =0 . Then the value of r is

Options

  1. A2 9 (p-q)(2 q-p)
  2. B2 9 (q-p)(2 p-q)
  3. C2 9 (q-2 p)(2 q-p)
  4. D2 9 (2 p-q)(2 q-p)

Correct answer

D. 2 9 (2 p-q)(2 q-p)

Step-by-step solution

and are the roots of x^2- p x+ r =0 sum of roots = + + =p...(i) 2 , 2 are the roots of x^2- q x+ r =0 sum of roots = q aligned & 2 +2 =q & +4 =2 q...(ii) aligned Subtracting (i) from (ii), we get aligned & 3 =2 q-p & = 2 q-p 3 aligned From (i), aligned & + 2 q-p 3 =p & = 2(2 p-q) 3 aligned Product of roots = aligned r= & = 2(2 p-q) 3 2 q-p 3 & = 2 9 (2 p-q)(2 q-p) aligned

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