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Manipal MET2017MathematicsQuadratic Equation

If x^2+p x+q=0 is the quadratic equation whose roots are a-2 and b-2 , where a and b are the roots of x^2-3 x+1=0 , then

Options

  1. Ap=1, q=5
  2. Bp=5, q=1
  3. Cp=1, q=1
  4. Dp=1, q=-1

Correct answer

D. p=1, q=-1

Step-by-step solution

Since, a and b are the roots of equation array rlrl x^2-3 x+1 & =0 array a+b=3 and a b=1 Now, the given roots are a-2 and b-2 aligned Sum of roots & =a-2+b-2 & =3-4=-1 aligned and products of roots =(a-2)(b-2) aligned & =a b-2(a+b)+4 & =1-6+4=-1 aligned Required equation is x^2+x-1=0 Which is equivalent to x^2+p x+q=0 p=1 and q=-1

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