A quadratic equation is given by $(a+b) x^2-(a+b+c) x+k=0$, where $a, b, c$ are real. If k = c, then the roots of the equation are:

• A

  $\frac{a+c}{a+b}$ and $\frac{b}{a+b}$
• B

  $\frac{a+c}{a+b}$ and $-\frac{b}{a+b}$
• Correct answer
  C

  1 and $\frac{c}{a+b}$
• D

  -1 and $-\frac{c}{a+b}$

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