9 The roots of the equation $$ x^{3}+6 x^{2}+10 x+14=0 $$ are $$ \alpha, \beta $$ and $$ \gamma $$. Find the equation whose roots are: (a) $$ \alpha^{2}, \beta^{2} $$ and $$ \gamma^{2} $$ (b) $$ \alpha+3, \beta+3 $$ and $$ \gamma+3 $$

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Ellis Hodgson · Accepted Answer

(a) The equation is $$ x^3 - 16x^2 - 68x - 196 = 0 $$. (b) The equation is $$ y^3 - 3y^2 + 5y + 11 = 0 $$.

9 The roots of the equation \( x^{3}+6 x^{2}+10 x+14=0 \) are \( \alpha, \beta \) and \( \gamma \). Find the equation whose roots are: (a) \( \alpha^{2}, \beta^{2} \) and \( \gamma^{2} \) (b) \( \alpha+3, \beta+3 \) and \( \gamma+3 \)

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9 The roots of the equation \( x^{3}+6 x^{2}+10 x+14=0 \) are \( \alpha, \beta \) and \( \gamma \). Find the equation whose roots are: (a) \( \alpha^{2}, \beta^{2} \) and \( \gamma^{2} \) (b) \( \alpha+3, \beta+3 \) and \( \gamma+3 \)

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