Discuss the nature of the roots of the equations $\displaystyle (a+c-b)x^{2}+2cx+(b+c-a)=0$

To determine the nature of the roots, we calculate the discriminant using the formula D = b^2 - 4ac. Substituting the coefficients gives D = (2c)^2 - 4(a+c-b)(b+c-a), which simplifies to 4c^2 - 4(c^2 - (a-b)^2) and further reduces to 4(a-b)^2. Since the square of any real number is always positive, the discriminant is greater than zero, indicating the roots are real and unequal.

• Thanks
• Wrong explanation