Find All The Zeroes Of The Polynomial $ 3x^{3}+10x^{2}-9x-4$, If One Of Its Zeroes Is 1.

Given:  The Polynomial $ 3x^{3}+10x^{2}-9x-4$

To do: Find all the zeros of the polynomial if one of its zero is 1

Solution:

One of the zeros of the given cubic polynomial is 1  (given)

Using Horner method dividing the polynomial

1 | 3  + 10  -9  -4

      0      3   13   4

   -----------------

     3      13   4    0

The quadratic factor of the cubic polynomial is $3x^{2} + 13x + 4$

= $3x^{2} + 12x + x + 4 = (3x + 1)(x + 4)$

So the other two zeros of the cubic polynomial are $\frac{-1}{3}$ and -4

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Updated on: 10-Oct-2022

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