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AP EAMCET2011MathematicsQuadratic Equation

If A and B are the roots of the quadratic equation x^2-p x+q=0 , then ^2(A+B) is equal to

Options

  1. Ap^2 p^2+q^2
  2. Bp^2 (p+q)^2
  3. C1- p (1-q)^2
  4. Dp^2 p^2+(1-q)^2

Correct answer

D. p^2 p^2+(1-q)^2

Step-by-step solution

Since, A and B are the roots of the equation x^2-p x+q=0 A+ B=p and A B=q aligned (A+B) & = A+ B 1- A B & = p 1-q aligned aligned & (A+B)= p p^2+(1-q)^2 & ^2(A+B)= p^2 p^2+(1-q)^2 & aligned

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