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 roots,we have $\alpha + \beta = p$ and $

Vedclass · Accepted Answer

$ \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 roots,we have $\alpha + \beta = p$ and $\alpha \beta = 8$.Given that the difference of the roots is $|\alpha - \beta| = 2$,so $(\alpha - \beta)^2 = 4$.We know the identity $(\alpha + \beta)^2 - (\alpha - \beta)^2 = 4\alpha \beta$.Substituting the known values: $p^2 - 2^2 = 4(8)$.$p^2 - 4 = 32$.$p^2 = 36$.Therefore,$p = \pm 6$.

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

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