Question

One zero of the polynomial 2x^3 - x^2 -13x -6 is

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Answer 1

SOLUTION

TO DETERMINE

One zero of the polynomial

$\sf 2 {x}^{3} - {x}^{2} - 13x - 6$

EVALUATION

Let p(x) be the given polynomial

Then we have

$\sf p(x) = 2 {x}^{3} - {x}^{2} - 13x - 6$

For Zero of the polynomial we have

p(x) = 0

$\sf \implies \: 2 {x}^{3} - {x}^{2} - 13x - 6 = 0$

$\sf \implies \: 2 {x}^{3} - 6 {x}^{2} + 5 {x}^{2} - 15x + 2x - 6 = 0$

$\sf \implies \: 2 {x}^{2} (x - 3) + 5x(x - 3) + 2(x - 3) = 0$

$\sf \implies \: (x - 3)(2 {x}^{2} + 5x + 2) = 0$

$\sf \implies \: (x - 3)(2 {x}^{2} + 4x + x + 2) = 0$

$\sf \implies \: (x - 3) \{ \:2x(x + 2) + 1(x + 2) \} = 0$

$\sf \implies \: (x - 3) \:(x + 2)(2x + 1) = 0$

$\displaystyle \sf \implies \: x = 3 \:, \: - 2 \: ,\: - \frac{1}{2}$

So three zeroes of the polynomial are

$\displaystyle \sf \ 3 \:, \: - 2 \: ,\: - \frac{1}{2}$

Hence one of zeroes of the polynomial is 3

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