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Manipal MET2015MathematicsQuadratic Equation

If A and B are the roots of the equation x^2-a x+b=0 , then the value of ^2(A+B) is

Options

  1. Aa^2 a^2+(1-b)^2
  2. Ba^2 a^2+b^2
  3. Ca^2 (a+b)^2
  4. Da^2 b^2+(1-a)^2

Correct answer

A. a^2 a^2+(1-b)^2

Step-by-step solution

Since, A and B are the roots of the equation x^2-a x+b=0 . Therefore, A+ B=a and A B=b Now, (A+B)= A+ B 1- A B = a 1-b Now, ^2(A+B)= 1 2 [1- 2(A+B)] aligned & ^2(A+B)= 1 2 1- 1- ^2(A+B) 1+ ^2(A+B) & ^2(A+B)= 1 2 1- 1- a^2 (1-b)^2 1+ a^2 (1-b)^2 & ^2(A+B)= 1 2 2 a^2 a^2+(1-b)^2 & ^2(A+B)= a^2 a^2+(1-b)^2 aligned

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