If the equations x^{2}+2x-3=0 and x^{2}+3x-k= | vedclass

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(D) Let $\alpha$ be the common root of the given equations.Then,$\alpha^{2}+2\alpha-3=0$ and $\alpha^{2}+3\alpha-k=0$.Subtracting the first equation f

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$4$

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(D) Let $\alpha$ be the common root of the given equations.Then,$\alpha^{2}+2\alpha-3=0$ and $\alpha^{2}+3\alpha-k=0$.Subtracting the first equation from the second:$(\alpha^{2}+3\alpha-k) - (\alpha^{2}+2\alpha-3) = 0$$\alpha - k + 3 = 0$$\alpha = k - 3$Substitute $\alpha = k - 3$ into the first equation $\alpha^{2}+2\alpha-3=0$:$(k-3)^{2} + 2(k-3) - 3 = 0$$k^{2} - 6k + 9 + 2k - 6 - 3 = 0$$k^{2} - 4k = 0$$k(k-4) = 0$Since $k$ is non-zero,$k = 4$.

If the equations $x^{2}+2x-3=0$ and $x^{2}+3x-k=0$ have a common root,then the non-zero value of $k$ is:

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