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tensa zangetsu [6.8K]
2 years ago
7

We want to find the zeros of this polynomial:

Mathematics
1 answer:
fredd [130]2 years ago
8 0

Answer:

x = -3 and x = -3/2

Step-by-step explanation:

After writing down the polynomial, split it; put a line between 3x^2 and -18x. Look and 2x^3 + 3x^2 and -18x - 27 separately and factor them both:

p(x) = 2x^3 + 3x^2 <u>- 18x -27</u>

p(x) = x^2(2x+3) <u>-9(2x+3)</u>

Now notice how x^2 and -9 have the same factor (2x+3). That means x^2 and -9 can go together:

p(x) = (x^2 - 9)(2x+3)

Factor it once more because there's a difference of squares:

p(x) = (x+3)(x-3)(2x+3)

Now just plug in whatever makes the each bracket equal 0:

x = -3, x = 3, and x = -3/2

Those are your zeros.

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Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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And p is the probability of X happening.

In this problem we have that:

n = 5, p = 0.517

Distribution

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{5,0}.(0.517)^{0}.(0.483)^{5} = 0.0263

P(X = 1) = C_{5,1}.(0.517)^{1}.(0.483)^{4} = 0.1407

P(X = 2) = C_{5,2}.(0.517)^{2}.(0.483)^{3} = 0.3012

P(X = 3) = C_{5,3}.(0.517)^{3}.(0.483)^{2} = 0.3224

P(X = 4) = C_{5,4}.(0.517)^{4}.(0.483)^{1} = 0.1725

P(X = 5) = C_{5,5}.(0.517)^{5}.(0.483)^{0} = 0.0369

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