The value of a for which the equations x^2 - | vedclass

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(D) Given equations are $x^2 - 3x + a = 0$ $(i)$ and $x^2 + ax - 3 = 0$ $(ii)$.Subtracting $(ii)$ from $(i)$,we get:$(x^2 - 3x + a) - (x^2 + ax - 3) =

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$2$

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(D) Given equations are $x^2 - 3x + a = 0$ $(i)$ and $x^2 + ax - 3 = 0$ $(ii)$.Subtracting $(ii)$ from $(i)$,we get:$(x^2 - 3x + a) - (x^2 + ax - 3) = 0$$-3x - ax + a + 3 = 0$$-(a + 3)x + (a + 3) = 0$$(a + 3)(1 - x) = 0$This implies either $a = -3$ or $x = 1$.If $a = -3$,the equations become $x^2 - 3x - 3 = 0$ and $x^2 - 3x - 3 = 0$,which are identical. However,for a unique value of $a$ typically sought in such problems,we consider the case where $x = 1$ is the common root.Substituting $x = 1$ into equation $(i)$:$1^2 - 3(1) + a = 0$$1 - 3 + a = 0$$a - 2 = 0$$a = 2$.

The value of $a$ for which the equations $x^2 - 3x + a = 0$ and $x^2 + ax - 3 = 0$ have a common root is

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