If alpha and beta are the roots of Ax^2 + Bx | vedclass

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(B) For the equation $Ax^2 + Bx + C = 0$,the sum of roots is $\alpha + \beta = -\frac{B}{A}$ and the product of roots is $\alpha\beta = \frac{C}{A}$.F

Vedclass · Accepted Answer

$\frac{2AC - B^2}{A^2}$

Vedclass · Answer

(B) For the equation $Ax^2 + Bx + C = 0$,the sum of roots is $\alpha + \beta = -\frac{B}{A}$ and the product of roots is $\alpha\beta = \frac{C}{A}$.For the equation $x^2 + px + q = 0$,the sum of roots is $\alpha^2 + \beta^2 = -p$ and the product of roots is $\alpha^2\beta^2 = q$.We know that $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta$.Substituting the values,we get $-p = (-\frac{B}{A})^2 - 2(\frac{C}{A})$.$-p = \frac{B^2}{A^2} - \frac{2C}{A} = \frac{B^2 - 2AC}{A^2}$.Therefore,$p = -\frac{B^2 - 2AC}{A^2} = \frac{2AC - B^2}{A^2}$.

If $\alpha$ and $\beta$ are the roots of $Ax^2 + Bx + C = 0$ and $\alpha^2$ and $\beta^2$ are the roots of $x^2 + px + q = 0$,then find the value of $p$.

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