The expressions x^2 - 11x + a and x^2 - 14x + | vedclass

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(B) Let the common factor be $(x - k)$. Then $k$ is a common root of the equations $x^2 - 11x + a = 0$ and $x^2 - 14x + 2a = 0$.Subtracting the two eq

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$0, 24$

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(B) Let the common factor be $(x - k)$. Then $k$ is a common root of the equations $x^2 - 11x + a = 0$ and $x^2 - 14x + 2a = 0$.Subtracting the two equations:$(x^2 - 11x + a) - (x^2 - 14x + 2a) = 0$$3x - a = 0 \Rightarrow x = \frac{a}{3}$.Substituting $x = \frac{a}{3}$ into the first equation:$(\frac{a}{3})^2 - 11(\frac{a}{3}) + a = 0$$\frac{a^2}{9} - \frac{11a}{3} + a = 0$$\frac{a^2}{9} - \frac{8a}{3} = 0$$a^2 - 24a = 0$$a(a - 24) = 0$Thus,$a = 0$ or $a = 24$.

The expressions $x^2 - 11x + a$ and $x^2 - 14x + 2a$ will have a common factor,if $a = $

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