Question

Find the zeroes of the cubic polynomial p(x)=x³-5x²-2x+24 give products of two zeroes is 12 and verify the relationship between the zeroes and the coefficients??


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Answer 1

It is a very easy question...

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So your answers are :-

Alpha = 4

Beta = 3

Gama = -2

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PLEASE REFER TO MY ATTACHMENT TO SEE THE EXPLANATION OF MY ANSWER

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Now lets verify the relationship between the zeroes..

1) ALPHA + BETA + GAMA = -(-5/1)

4 + 3 -2 = 5

7 - 2 = 5

5 = 5

Hence proved

2) Alpha×Beta + Beta×Alpha + Gama×Alpha = -2

12 + (-6) + (-8) = (-2)

12 -6-8 = (-2)

12 - 14 = (-2)

-2 = -2

hence proved

3) Alpha × Beta × Gama = -24

4 ×3×(-2) = -24

12 × (-2) = -24

-24 = -24

Hence proved .

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