If alpha, beta, gamma are the roots of the eq | vedclass

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(B) Given that $\alpha, \beta, \gamma$ are the roots of $4x^3 + 12x^2 - 7x + 165 = 0$. From Vieta's formulas: $\alpha + \beta + \gamma = -\frac{12}{4}

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(B) Given that $\alpha, \beta, \gamma$ are the roots of $4x^3 + 12x^2 - 7x + 165 = 0$. From Vieta's formulas: $\alpha + \beta + \gamma = -\frac{12}{4} = -3$ $\alpha\beta + \beta\gamma + \gamma\alpha = -\frac{7}{4}$ $\alpha\beta\gamma = -\frac{165}{4}$ We need to find the product of the roots of the second equation,which is $(\alpha + 5)(\beta + 5)(\gamma + 5)$. Expanding this expression: $(\alpha + 5)(\beta + 5)(\gamma + 5) = \alpha\beta\gamma + 5(\alpha\beta + \beta\gamma + \gamma\alpha) + 25(\alpha + \beta + \gamma) + 125$ Substituting the values: $= -\frac{165}{4} + 5(-\frac{7}{4}) + 25(-3) + 125$ $= -\frac{165}{4} - \frac{35}{4} - 75 + 125$ $= -\frac{200}{4} + 50$ $= -50 + 50 = 0$

If $\alpha, \beta, \gamma$ are the roots of the equation $4x^3 + 12x^2 - 7x + 165 = 0$ and $\alpha + 5, \beta + 5, \gamma + 5$ are the roots of the equation $ax^3 + bx^2 + cx + d = 0$,then the product of the roots of the second equation is:

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