Q151 / 270 · NDA 2012 (Phase 2) · Mathematics

If the roots of a quadratic equation are $m+n$ and $m-n$, then the quadratic equation will be :

  • A
    $x^2+2 m x+m^2-m n+n^2=0$
  • B
    $x^2+2 m x+(m-n)^2=0$
  • Correct answer
    C
    $x^2-2 m x+m^2-n^2=0$
  • D
    $x^2+2 m x+m^2-n^2=0$

Solution

$\because$ Roots are $m+n$ and $m-n$ Sum of roots $=m+n+m-n=2 m$ Product of roots $=(m+n)(m-n)=m^2-n^2$ $x^2-($ Sum of roots $) x+$ Product of roots $=0$ $x^2-2 m x+m^2-n^2=0$

Hence, the correct answer is option: 'C'.

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