If a, b, c are real, then both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are always
(A) positive (B) negative (C) real (D) imaginary

Question

If a, b, c are real, then both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are always (A) positive (B) negative (C) real (D) imaginary

Saurabh Koranglekar · Answer

Dear student The answer is option c Regards

Vikas TU · Answer

Refer https://www.askiitians.com/iit-jee-algebra/quadratic-equations-and-expressions/interval-in-which-the-roots-lie.aspx

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If a, b, c are real, then both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are always (A) positive (B) negative (C) real (D) imaginary

If a, b, c are real, then both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are always
(A) positive (B) negative (C) real (D) imaginary

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If a, b, c are real, then both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are always (A) positive (B) negative (C) real (D) imaginary

If a, b, c are real, then both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are always (A) positive (B) negative (C) real (D) imaginary

2 Answers

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If a, b, c are real, then both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are always
(A) positive (B) negative (C) real (D) imaginary