If the difference of the roots of x^2 - px + | vedclass

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(C) Let the roots of the quadratic equation $x^2 - px + 8 = 0$ be $\alpha$ and $\beta$.From the properties of quadratic equations,the sum of the roots

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$ \pm 6$

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(C) Let the roots of the quadratic equation $x^2 - px + 8 = 0$ be $\alpha$ and $\beta$.From the properties of quadratic equations,the sum of the roots is $\alpha + \beta = p$ and the product of the roots is $\alpha \beta = 8$.We are given that the difference of the roots is $|\alpha - \beta| = 2$,which implies $(\alpha - \beta)^2 = 4$.Using the identity $(\alpha + \beta)^2 - (\alpha - \beta)^2 = 4\alpha \beta$,we substitute the known values:$p^2 - 2^2 = 4(8)$$p^2 - 4 = 32$$p^2 = 36$$p = \pm 6$.

If the difference of the roots of $x^2 - px + 8 = 0$ is $2$,then the value of $p$ is

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