If k=c, then the roots of the equation are:

A quadratic equation is given by (a+b)x^{2}-(a+b+c)x+k=0, where a, b, c are real.

  1. A. \frac{a+c}{a+b} and \frac{b}{a+b}
  2. B. \frac{a+c}{a+b} and -\frac{b}{a+b}
  3. C. 1 and \frac{c}{a+b} ✓
  4. D. -1 and -\frac{c}{a+b}

Correct Answer: C. 1 and \frac{c}{a+b}

Explanation

For k=c, the equation is (a+b)x^2 - (a+b+c)x + c = 0. We can observe that x=1 is a root since (a+b)(1)^2 - (a+b+c)(1) + c = 0. The product of the roots is given by \frac{\text{constant term}}{\text{leading coefficient}} = \frac{c}{a+b}. If one root is 1, the other root must be \frac{c}{a+b}.

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