Question

$\huge \mathbb \color{lime}{Question:}$
Find the rational roots of the polynomial
$f(x) \: 2x³+ 3x²- 11x - 6.$

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Answer 1

Step-by-step explanation:

First, note that x=3 is a solution to the equation. This being the case, x-3 is a factor. So:

2x³-3x²-11x+6/x-3=2x²+3x-2

2x³-3x²-11x+6=(x-3)(2x²+3x-2)

2x²+3x-2=(2x-1)(x+2)

2x³-3x²-11x+6=(x-3)(2x-1)(x+2)=0

Then:

x=3, 1/2, or -2

Answer 2

ANSWER (☞^o^) ☞First note:That X=3 is a solution of

the equation this being the case

X-3is a Factor

So,

Step-by-step explaition :-

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

$2x {}^{3} - 3 \times 2 - 11 \times + 6(x - 3)(2 \times {}^{2} + 3 \times 2)$

$2 \times {}^{2} + 3x - 2 = (2 \times - 1) \\ (x + 2)$

$2 \times {}^{2} - 3 \times 2 - 11 \times 6 = \\ ( \times - 3)(2 \times - 1)(x + 2) = 0$

Then,

X=3, 1/2,or-2.

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