Discuss the nature of the roots of the equation:
$(b + c) x^{2} - (a + b + c) x + a = 0$

Real and equal

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Real and unequal

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Imaginary

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None of these

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Solution

The correct option is B Real and unequal
$(b + c) x^{2} - (a + b + c) x + a = 0 D = B^{2} - 4 A C = {(a + b + c)}^{2} - 4 (a (b + c)) = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a - 4 (a b + a c) = a^{2} + b^{2} + c^{2} - 2 a b - 2 a c + 2 b c = {(a - b - c)}^{2} > 0$
Hence, the roots are real and unequal

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