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Nikitich [7]
3 years ago
7

What is 5.1234 roundd to the thousands

Mathematics
1 answer:
Sveta_85 [38]3 years ago
8 0
5.1234 to the nearest thousandths is 5.123
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One root of f(x) = 2x3 9x2 7x – 6 is –3. explain how to find the factors of the polynomial.
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<span>We have the following polynomial:

f(x)=2x^{3}+9x^{2}+7x-6

The problem states that one root is -3. Thus, it is true that (x+3) is a factor of the polynomial. Given that this is fulfilled, it is also true that:

</span>f(x)=(x+3)Q(x) \therefore Q(x)=\frac{f(x)}{x+3} \\ \\ where \ Q(x) \ has \ a \ degree \ of \ 2<span>

We can find Q(x) by applying Ruffini's rule, thus:

</span>\ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 9 \ \ \ \ \ \ \ \ 7 \ \ \ \ \ \ -6  \\ -3 \\ \rule{50mm}{0.1mm} \\ \ {} \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 3 \ \ \ \ \ -2 \ \ \ \ \ \ \ \ 0<span>

Therefore:

Q(x)=2x^{2}+3x-2

The roots of this polynomial can be get as follows:

x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \rightarrow x_{12}=\frac{-3\pm\sqrt{3^2-4(2)(-2)}}{2(2)}\\x_{1}=\frac{1}{2};\ x_{2}=-2

These are the roots along with -3. Finally, the factored polynomial can be written as follows:

f(x)=(x+3)(x+2)(2x-1)</span>
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What event led Machiavelli to begin thinking about how governments should operate?
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Machiavelli promoted the idea that a ruler should be gentle most of the time, but when necessary the ruler must make use of any form of manipulation, deceit, and even murder to achieve his ends.

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