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Manipal MET2020MathematicsQuadratic Equation

The quadratic equation whose roots are 1 3+ 2 and 1 3- 2 , will be

Options

  1. A7 x^2-6 x+1=0
  2. B6 x^2-7 x+1=0
  3. Cx^2-6 x+7=0
  4. Dx^2-7 x+6=0

Correct answer

A. 7 x^2-6 x+1=0

Step-by-step solution

Given roots are 1 3+ 2 and 1 3- 2 aligned & i.e. 1 (3+ 2 ) (3- 2 ) (3- 2 ) & and 1 (3- 2 ) (3+ 2 ) (3+ 2 ) & 3- 2 7 and 3+ 2 7 aligned So, the required quadratic equation is x^2- (Sum of the roots) x + Product of the roots =0 aligned & x^2- [ 3- 2 7 + 3+ 2 7 ] x &+ ( 3- 2 7 ) ( 3+ 2 7 )=0 aligned aligned & x^2- ( 6 7 ) x+ 9-2 49 =0 & x^2- 6 7 x+ 7 49 =0 7 x^2-6 x+1=0 aligned

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