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AP EAMCET202125 Aug 2021Evening ShiftMathematicsQuadratic EquationActual

The condition that x^3-p x^2+q x-r=0 may have two of its roots equal to each other but of opposite sign is

Options

  1. Ar = pq
  2. Br=2 p^3+p q
  3. Cr=p^2 q
  4. Dr=p^2 q^2

Correct answer

A. r = pq

Step-by-step solution

Given equation, x^3-p x^2+q x-r=0 ...(i) Let , and are the roots of Eq. (i) Hence, array r + + = -(-p) 1 =p ...(ii) + + =q ...(iii) =-(-r)=r..._(iv) array Given that, two roots are equal and opposite in sign. Let =- From Eq. (ii), we get, + + =p aligned - + + & =p & =p...(v) aligned From Eq. (iv), we get, =r aligned - ^2 & =r - ^2 p & =r ^2 & = -r p aligned From Eq. (iii), we get aligned + + & =q - ^2+ p+(- ) p & =q r p +0=q aligned r=p q

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