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Relation between Roots and Coefficients for Higher Order Equations

Find the prod...

Question

Find the product of all the roots for the equation $3 x^{3} + 5 x^{2} + 9 x = 0$ .
__

A

0.0

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B

zero

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C

Zero

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D

00

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E

0

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Solution

Compare $3 x^{3} + 5 x^{2} + 9 x = 0$ by standard form of cubic equation $a x^{3} + b x^{2} + c x + d = 0$ .
We have a = 3, b = 5, c = 9 and d = 0

Using the relation between roots and coefficients, we get
Product of the roots $α β γ = - \frac{d}{a} = 0$

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