For an equation $x^{3} - 8 x^{2} + 4 x + 7 = 0$ , what is the value of the product of all the roots?

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Solution

The correct option is A $- 7$
Given equation is $x^{3} - 8 x^{2} + 4 x + 7 = 0$
Let the roots be $a, b, c$
According to the relation between the roots and coefficients of equations of degree $3$ , the product of all the roots is $- \frac{constant term}{coefficient of x^{3}}$ ,
we can say that $a b c = \frac{- 7}{1} = - 7$

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