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(D) Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^{2}+kx+12=0$.From the properties of roots,we have the sum of roots $\alpha+\bet

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$\pm 7$

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(D) Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^{2}+kx+12=0$.From the properties of roots,we have the sum of roots $\alpha+\beta = -k$ and the product of roots $\alpha\beta = 12$.We are given that $\alpha-\beta = 1$.We know the identity $(\alpha-\beta)^{2} = (\alpha+\beta)^{2} - 4\alpha\beta$.Substituting the known values into the identity:$(1)^{2} = (-k)^{2} - 4(12)$$1 = k^{2} - 48$$k^{2} = 49$$k = \pm 7$.

If $\alpha, \beta$ are the roots of the equation $x^{2}+kx+12=0$ such that $\alpha-\beta=1$,the value of $k$ is

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