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Andru [333]
3 years ago
6

What are potential roots of p(x) = x4 + 22x2 – 16x – 12

Mathematics
2 answers:
kow [346]3 years ago
8 0
Simplify <span>22\times 2<span>22×2</span></span> to <span>44<span>44</span></span>
<span><span>{x}^{4}+44-16x-12<span><span>x<span><span>​4</span><span>​​</span></span></span>+44−16x−12</span></span>Collect like terms
<span><span>{x}^{4}+(44-12)-16x<span><span>x<span><span>​4</span><span>​​</span></span></span>+(44−12)−16x</span></span> Simplify</span><span><span>{x}^{4}+32-16x<span><span>x<span><span>​4</span><span>​​</span></span></span>+32−16x</span></span><span>
</span></span></span>
rjkz [21]3 years ago
4 0

Answer:

±1, ±2, ±3, ±4, ±6 and ±12

Step-by-step explanation:

The potential roots are obtained as following:

potential roots = factors of the constant term / factors of leading coefficient

The constant term is -12, its factors are ±1, ±2, ±3, ±4, ±6 and ±12

The leading coefficient is 1, its factors are  ±1

Therefore the potential roots are ±1, ±2, ±3, ±4, ±6 and ±12

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Several years​ ago, 39​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students r
BaLLatris [955]
<h2>Answer with explanation:</h2>

Let p be the population proportion  of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive.

Given : Several years​ ago, 39​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive.

Set hypothesis to test :

H_0: p=0.39\\\\H_a :p\neq0.39

Sample size : n= 1055

Sample proportion : \hat{p}=\dfrac{466}{1055}=0.441706161137\approx0.44

Critical value for 95% confidence : z_{\alpha/2}=1.96

Confidence interval : \hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}

0.44\pm (1.96)\sqrt{\dfrac{0.39(1-0.39)}{1055}}\\\\0.44\pm0.0299536805135\\\\0.44\pm0.03\\\\=(0.44-0.03, 0.44+0.03)\\\\=(0.41,\ 0.47)

Since , Confidence interval does not contain 0.39.

It means we reject the null hypothesis.

We conclude that 95​% confidence interval represents evidence that​ parents' attitudes toward the quality of education have changed.

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Answer:

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Step-by-step explanation:

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