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3 years ago

Write a polynomial function of least degree with the given zero. -1+ √ 2, √ 3

Mathematics

1 answer:

kirill115 [55]3 years ago

6 0

Answer:

f(x) = $x^{4}$ + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + $\sqrt{2}$ is a zero then - 1 - $\sqrt{2}$ is also a zero

$\sqrt{3}$ is a zero then - $\sqrt{3}$ is also a zero

Thus the corresponding factors are

(x - (- 1 + $\sqrt{2}$ ) ), (x - (- 1 - $\sqrt{2}$ ) ), (x - $\sqrt{3}$ ), (x - (- $\sqrt{3}$ )), that is

(x + 1 - $\sqrt{2}$ ), (x + 1 + $\sqrt{2}$ ), (x - $\sqrt{3}$ ), (x + $\sqrt{3}$ )

The polynomial is then the product of the roots

f(x) = (x + 1 - $\sqrt{2}$ )(x + 1 + $\sqrt{2}$ )(x - $\sqrt{3}$ )(x + $\sqrt{3}$ )

= ((x + 1)² - ( $\sqrt{2}$ )²)((x² - ( $\sqrt{3}$ )²)

= (x² + 2x + 1 - 2)(x² - 3)

= (x² + 2x - 1)(x² - 3) ← distribute

= $x^{4}$ - 3x² + 2x³ - 6x - x² + 3

= $x^{4}$ + 2x³ - 4x² - 6x + 3

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Henry is conducting an experiment with 800 bacteria. He found the exponential growth rate to be 2.7% per hour. What is the amoun

joja [24]

Let's formulate an equation first. For exponential growth, we follow the formula. b = 800, r - 0.027. Hence,

y = 800(1+0.027)^t

Then, at t = 21, y will be determined
y = 800 (1+0.027)^21
y = 1399.81 = 1400

Thus, the amount of bacteria present after 21 hours is 1400.

8 0

3 years ago

A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the pr

Igoryamba

Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.

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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Random voting:

So 50% of voting yes, 50% no, so $p = 0.5$

15 members:

This means that $n = 15$

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

$p = P(X = 0) + P(X = 15)$

In which

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

$P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003$

$P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003$

$p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006$

0.006% probability that the final vote count is unanimous.

7 0

3 years ago

What is the simple way of solving quadratic equation

aleksandrvk [35]

quadratic equations can be soled by 3 methods

factorization

completing square

quadratic formula

but factorization is the simplest

4 0

3 years ago

4. Which of the following indicates the multiplication property of equality when solving Vz= 5?

tiny-mole [99]

Answer:

D. 21.

Step-by-step explanation:

The general form of the equation of a circle is:

(x - a)^2 + (y - b)^2 = r^2 where r is the radius.

Comparing:

(x + 5)^2 + (y + 7)^2 = 21^2

So r^2 = 21^2

making r = √21^2

= 21.

plz make me brainliest

3 0

3 years ago

What is the elimination to this solution i think its b

Blababa [14]

EXPLANATION:

To get the solution of the simultaneous equation, using the elimination method:

We will have the following steps:

Step 1:

Write the two equations:

$\begin{gathered} y=-\frac{1}{2}x+3 \\ y=-\frac{7}{2}x-3 \end{gathered}$

Step2: Subtract the two equations:

$\begin{gathered} y-y=-\frac{1}{2}x-(-\frac{7}{2}x)+3-(-3) \\ 0=-\frac{1}{2}x+\frac{7}{2}x+6 \\ \end{gathered}$

Step 3: Simplify the expression

$\begin{gathered} 0=3x+6 \\ 3x=-6 \\ x=-\frac{6}{3} \\ x=-2 \end{gathered}$

Step 4: Substitute x=-2 into the formula:

$\begin{gathered} y=-\frac{1}{2}x+3 \\ y=-\frac{1}{2}\times-2+3 \\ y=1+3 \\ y=4 \end{gathered}$

Therefore, the answer is

$(-2,4)$

Thus,

Option B is correct

5 0

1 year ago