Let $f(x) = x^{3} - 3x + b$ and $g(x) = x^{2} + bx - 3$, where b is a real number. If the equations

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Let $f(x) = x^{3} - 3x + b$ and $g(x) = x^{2} + bx - 3$, where b is a real number. If the equations $f(x) = 0$ and $g(x) = 0$ have a common root, then

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Let x be the common root of equation.$$\begin{array}{r} x^{3} - 3x + b = 0\#(1) \ x^{2} + bx - 3 = 0\#(2) \end{array}$$(2) $	imes x -$ (1) $\Rightarrow {bx}^{2} - b = 0 \Rightarrow 	ext{ }b = 0$ or $x = \pm 1$.$$\begin{matrix} 	ext{~Put~} & x = 1, \Rightarrow b = 2 \ & x = - 1, \Rightarrow b = - 2 \ 	herefore & b = 0,2, - 2 \end{matrix}$$

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