Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots 5 and 2?

2 answers:

6 0

A root of a polynomial doesn't mean it is a square root of!!!!!!

P(x)=3(x-5)(x-2)=3x²-21x+30

f (x)= 3 x power point 2 - 21 x + 30

Alex Ar [27]2 years ago

4 0

Answer:

the polynomial is: $3x^2-21x+30$

Step-by-step explanation:

we know that the polynomial function p(x) of lowest degree with roots as 'a' and 'b' and leading coefficient as 'c' is given by: $p(x)=c(x-a)(x-b)$

here we are given that the roots are 5 and 2 and the leading coefficient is 3.

so the polynomial p(x) of lowest degree with the above properties is: $p(x)=3(x-5)(x-2)$

$p(x)=3(x^2-5x-2x+10)$

$p(x)=3(x^2-7x+10)$

$p(x)=3x^2-21x+30.$ .

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Let us convert all figures into decimals so that we can compare them easily.

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7 0

2 years ago

Two different samples will be taken from the same population of test scores where the population mean and standard deviation are

Alenkinab [10]

Answer:

The sample consisting of 64 data values would give a greater precision.

Step-by-step explanation:

The width of a (1 - α)% confidence interval for population mean μ is:

$\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}$

So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).

That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.

Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.

The two sample sizes are:

n₁ = 25

n₂ = 64

The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.

Width for n = 25:

$\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]$