If the product of the roots of 9x^3 + 112x^2 | vedclass

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Question

(C) Given the cubic equation: $9x^3 + 112x^2 - 120x + a = 0$. Let the roots be $\alpha, \beta, \gamma$. The product of the roots is given as $\alpha \

Vedclass · Accepted Answer

$-108$

Vedclass · Answer

(C) Given the cubic equation: $9x^3 + 112x^2 - 120x + a = 0$. Let the roots be $\alpha, \beta, \gamma$. The product of the roots is given as $\alpha \beta \gamma = 12$. For a cubic equation $Ax^3 + Bx^2 + Cx + D = 0$,the product of the roots is given by the formula $\alpha \beta \gamma = -\frac{D}{A}$. Here,$A = 9$ and $D = a$. Substituting the values,we get: $-\frac{a}{9} = 12$. Multiplying both sides by $9$,we get: $-a = 12 	imes 9 = 108$. Therefore,$a = -108$.

If the product of the roots of $9x^3 + 112x^2 - 120x + a = 0$ is $12$,then the value of '$a$' is

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