If each pair of the equation ${x^2} + ax + b = 0,\;{x^2} + bx + c = 0\;\,\,{\rm{and}}\,\;{x^2} + cx + a = 0$ has a common root, then product of all common roots is

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

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Analyzing +4 | -1

If each pair of the equation

{x^2} + ax + b = 0,\;{x^2} + bx + c = 0\;\,\,\mathrm{and}\,\;{x^2} + cx + a = 0

has a common root, then product of all common roots is

View answer and explanation

Correct option: A

\sqrt {abc}

Option A is correct because the product of all common roots is

\sqrt{abc}

, which is derived from Vieta's formulas applied to the given equations.

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