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Sum of n Terms

If α, β, γ ...

Question

If $α, β, γ$ are the zeroes of $x^{3} - 5 x^{2} - 2 x + 24$ and $α β = 12$ , then $γ =$

A

2

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B

- 2

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C

3

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D

- 3

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Solution

The correct option is B $- 2$
If $α, β, γ$ are the zeroes of the cubic polynomial $a x^{3} + b x^{2} + c x + d$ , then
product of its zeroes, $α β γ = - \frac{d}{a}$

We know that,
$α β γ = - \frac{d}{a}$
$12 γ = - \frac{24}{1}$
[ $∵ α β = 12$ ]
$γ = - \frac{24}{12}$
$γ = - 2$
The correct answer is -2.

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