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Zeroes of a Polynomial

If α, β and γ...

Question

If $α, β$ and $γ$ are the zeroes of the polynomial $x^{3} - 5 x^{2} - 2 x + 24$ , which of the following is the difference of two zeroes?

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Solution

The correct option is A
By inspection, (-2) is a root of the equation $x^{3} - 5 x^{2} - 2 x + 24$
$= x^{3} + 2 x^{2} - 7 x^{2} - 14 x + 12 x + 24$
$= (x + 2) \times (x^{2} - 7 x + 12)$
$= (x + 2) \times (x - 3) \times (x - 4)$
therefore, the roots of the equation are -2, 3,4. Difference of 3 and 4 = 1

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