2023 · Q49
A quadratic equation is given by (a + b + c)x² − (2a + 2b)x + (a + b − c) = 0, where a, b and c are real and distinct. What are the roots of the equation?
Elementary MathematicsAlgebra
- A1, (a + b − c)/(a + b + c)
- B1, (a − b + c)/(a + b + c)
- C−1, (−a − b + c)/(a + b + c)
- D−1, (a + b − c)/(a + b + c)
Explanation
x=1 is a root: (a+b+c)-(2a+2b)+(a+b-c)=0; product of roots=(a+b-c)/(a+b+c), so other root=(a+b-c)/(a+b+c). With distinct reals, nature ... Option (a).