What are the roots of the equation?
Consider the following for the next two (02) items that follow : A quadratic equation is given by (a+b+c)x^2-(2a+2b)x+(a+b-c)=0; where a, b and c are real and distinct.
- A. 1, \frac{(a+b-c)}{(a+b+c)} ✓
- B. 1, \frac{(a-b+c)}{(a+b+c)}
- C. - 1, \frac{(-a-b+c)}{(a+b+c)}
- D. - 1, \frac{(a+b-c)}{(a+b+c)}
Correct Answer: A. 1, \frac{(a+b-c)}{(a+b+c)}
Explanation
Substitute x=1 into the equation: (a+b+c) - (2a+2b) + (a+b-c) = 0, so 1 is a root. The product of the roots is \frac{a+b-c}{a+b+c}. Since one root is 1, the other root must be \frac{a+b-c}{a+b+c}.
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