2 years ago

Given f(x)=x^3+2x+k. and x+1 is a factor of f(x), then what is the value of k?

Mathematics

1 answer:

Ludmilka [50]2 years ago

4 0

Answer:

k = 3.

Step-by-step explanation:

By the Factor Theorem. if x+a is a factor of f(x) then f(-a) = 0.

Here we use f(-1):

f(-1) = (-1)^3 + 2(-1) + k = 0

-1 - 2 + k = 0

k = 3.

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aev [14]

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Step-by-step explanation:

We are given that the random variable X has a binomial distribution with the given probability of obtaining a success. Also, given n = 6, p = 0.3.

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$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6

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p = probability of success which in our question is 0.3.

LET X = a random variable

So, it means X ~ $Binom(n=6, p=0.3)$

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P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{6}{0}0.3^{0} (1-0.3)^{6-0}+ \binom{6}{1}0.3^{1} (1-0.3)^{6-1}+ \binom{6}{2}0.3^{2} (1-0.3)^{6-2}$

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Therefore, P(X < 3) = 0.7443.

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3 years ago