Find all other zeroes of the polynomial $p (x) = 2 x^{3} + 3 x^{2} - 11 x - 6.$ if one of its zero is $- 3.$ Solve the equation by graphically method:-

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Solution

Given ,

$x = - 3$ is zero of given polynomial

$x + 3 = 0$

Now ,

$\frac{p (x)}{x + 3} = \frac{2 x^{2} - 3 x - 2}{x - 3}$

$\frac{2 x^{3} + 3 x - 11 x - 6}{x - 3} = 2 x^{2} - 3 x - 2$

$2 x^{2} - 4 x + x - 2 = 0$

$2 x (x - 2) + 1 (x - 2) = 0$

$(2 x + 1) (x - 2) = 0$

When ,

$2 x + 1 = 0$

$x = - \frac{1}{2}$

When,

$x - 2 = 0$

$x = 2$

Hence others two zeroes are $2, - \frac{1}{2}$ .

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