The roots of the following quadratic equation Real and unequal. $(b + c)x^2$ - (a + b + c) x + a = 0

To determine the nature of the roots, we evaluate the discriminant D = b^2 - 4ac for the equation (b + c)x^2 - (a + b + c)x + a = 0. Substituting the coefficients gives D = [-(a + b + c)]^2 - 4(b + c)(a), which expands to a^2 + b^2 + c^2 + 2ab + 2ac + 2bc - 4ab - 4ac. This simplifies to a^2 + b^2 + c^2 - 2ab - 2ac + 2bc, which perfectly factors into the square (a - b - c)^2. Since any squared term is always non-negative, D >= 0, meaning the roots are real and unequal as long as a does not equal b + c (which would make D = 0). Therefore, the statement is True.

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