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

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
$(a + c - b) x^{2} + 2 c x + (b + c - a) = 0 D = B^{2} - 4 A C = {(2 c)}^{2} - 4 (b + c - a) (a + c - b) = 4 c^{2} - 4 (a b + c b - b^{2} + a c + c^{2} - c b - a^{2} - a c + a b) = 4 c^{2} + 4 b^{2} + {4 a}^{2} - {4 c}^{2} - 8 a b = {4 a}^{2} + {4 b}^{2} - 8 a b = 4 {(a - b)}^{2} > 0$
Hence roots are real and unequal

Suggest Corrections

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