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Relationship Between Zeroes and Coefficients of a Cubic Polynomial

If α, β, γ ...

Question

If $α, β, γ$ are the zeros of the cubic polynomial $p (x) = x^{3} + 2 x^{2} - 3 x$ then $α \cdot β \cdot γ =$ _____

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Solution

The correct option is A $0$
Given,
$α, β, γ$ are the zeros of the cubic polynomial $p (x) = x^{3} + 2 x^{2} - 3 x + 0$ .
That means $α, β, γ$ are the root of the equation $x^{3} + 2 x^{2} - 3 x + 0 = 0$ .
Now from the relation between the roots and co-efficients we get,
$α . β . γ = - \frac{0}{1} = 0$ .

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