If the roots of the equation x^2 + px + q = 0 | vedclass

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(B) Let the roots of the equation be $\alpha$ and $\beta$.Given that the difference between the roots is $\alpha - \beta = 1$.We know the identity $(\

Vedclass · Accepted Answer

$p^2 = 4q + 1$

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(B) Let the roots of the equation be $\alpha$ and $\beta$.Given that the difference between the roots is $\alpha - \beta = 1$.We know the identity $(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta$.From the quadratic equation $x^2 + px + q = 0$,we have the sum of roots $\alpha + \beta = -p$ and the product of roots $\alpha\beta = q$.Substituting these values into the identity:$(1)^2 = (-p)^2 - 4(q)$$1 = p^2 - 4q$Therefore,$p^2 = 4q + 1$.

If the roots of the equation $x^2 + px + q = 0$ differ by $1$,then:

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