Question

If 1 is zero of polynomial 3x3 - x 2 -3x + 1, find the other zeroes

Answer 1

Hope this helps you. .

THANK YOU. .

Answer 2

The other zeros are -1, 1/3

Solution:

Given polynomial equation is:

$3x^3 - x^2 -3x+1$

We have to find the zeros of polynomial

From given,

$3x^3 - x^2 -3x+1$

$\text{Group the equation }\\\\(3x^3 - x^2 ) - (3x - 1)$

$\text{Take } x^2 \text{ as common term from first group }$

$x^2(3x - 1) - 1(3x- 1)\\\\Factor\ out\ the\ term\ 3x-1\\\\(3x - 1)(x^2 - 1) = 0\\\\(3x-1)(x+1)(x-1) = 0$

Therefore,

$x + 1 = 0\\\\x = -1\\\\x - 1 = 0\\\\x = 1\\\\3x - 1 = 0$

$x = \frac{1}{3}$

Thus the other zeros are -1, 1/3

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