Mathematics: 4. Find a third-degree polynomial equation with rational coefficients that has roots 4 and 6+i. A x^3- 8x^2 - 11x + 148 = 0 B x3 - 8x^2 - 12x + 37 = 0 C x^3 - 12x^2 + 37x = 0 D x^3 - 8x^2 - 11x = 0

For this case we have the following expression:We rationalize the second term multiplying by:So, we have:6...

4. Find a third-degree polynomial equation with rational

Ответ:

kayal1076

12.05.2022

Mathematics

For this case we have the following expression:

$3 + 2 \sqrt {2} + \frac {1} {3 + 2 \sqrt {2}} =$

We rationalize the second term multiplying by:

$\frac {3-2 \sqrt {2}} {3-2 \sqrt {2}}:$ $\frac {1} {3 + 2 \sqrt {2}} * \frac {3-2 \sqrt {2}} {3-2 \sqrt {2}} = \frac {3-2 \sqrt {2} } {9-6 \sqrt {2} +6 \sqrt {2} -4 (\sqrt {2}) ^ 2} = \frac {3-2 \sqrt {2}} {9-4 * 2} = \frac {3-2 \sqrt {2}} {1} = 3-2 \sqrt {2}$

So, we have:

$3 + 2 \sqrt {2} + 3-2 \sqrt {2} = 3 + 3 = 6$

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4. Find a third-degree polynomial equation with rational coefficients that has roots 4 and 6+i. A x^3- 8x^2 - 11x + 148 = 0
B x3 - 8x^2 - 12x + 37 = 0
C x^3 - 12x^2 + 37x = 0
D x^3 - 8x^2 - 11x = 0

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