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

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(B) Let the roots of the equation $x^2 + px + q = 0$ be $\alpha$ and $\beta$.Given that the difference between the roots is $\alpha - \beta = 1$.We kn

Vedclass · Accepted Answer

$p^2 = 4q + 1$

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(B) Let the roots of the equation $x^2 + px + q = 0$ be $\alpha$ and $\beta$.Given that the difference between the roots is $\alpha - \beta = 1$.We know that for a quadratic equation $ax^2 + bx + c = 0$,the sum of roots $\alpha + \beta = -b/a$ and the product of roots $\alpha\beta = c/a$.For the given equation,$\alpha + \beta = -p$ and $\alpha\beta = q$.Using the identity $(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta$,we substitute the known values:$(1)^2 = (-p)^2 - 4(q)$.$1 = p^2 - 4q$.Therefore,$p^2 = 4q + 1$.

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

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