All categories

3 years ago

Resolve in factors. I) x⁴+x²+1

Mathematics

2 answers:

stealth61 [152]3 years ago

7 0

Answer:

(x2−x+1)(x2+x+1)

Step-by-step explanation:

Let’s multiply by x2−1

(x4+x2+1)(x2–1)=x6+x4+x2−x4−x2−1=x6−1

So x4+x2+1=x6−1x2−1 .

Now, let’s factorize x6−1 differently: x6−1=(x3+1)(x3−1) . Also x2−1=(x+1)(x−1) .

So x4+x2+1=(x3+1)(x3−1)(x+1)(x−1)=x3+1x+1⋅x3−1x−1 .

Now, I can factorize x3+1=(x+1)(x2−x+1) and x3−1=(x−1)(x2+x+1) .

So. x4+x2+1=(x2−x+1)(x2+x+1) .

masha68 [24]3 years ago

6 0

Answer:

let a = x² (a ≥ 0), we have the equation:

a² + a + 1 = 0

⇔ a² + 2.1/2.a + 1/4 + 3/4 = 0

⇔ (a + 1/2)² = -3/4 (unreasonable)

=> no solutions

Step-by-step explanation:

You might be interested in

A sequence is defined by the function f(n)=f(n-1)+5. Where n represents the number of the term for n>1 and f(1)=-4. What are

Neporo4naja [7]

Answer:

The first four terms of the above sequence are 1, 6, 11, 16.

Step-by-step explanation:

A sequence is defined by the function f(n)=f(n-1)+5.

Where n represents the number of the term for n>1

First Put n = 2

f(2)=f(2-1)+5.

= f (1) + 5

= -4 + 5

= 1

Second Put n = 3

f(3)=f(3-1)+5.

= f (2) + 5

= 1 + 5

= 6

Third Put n = 4

f(4)=f(4-1)+5.

= f (3) + 5

= 6+ 5

= 11

Second Put n = 5

f(5)=f(5-1)+5.

= f (4) + 5

= 11 + 5

= 16

Therefore the first four terms of the above sequence are 1, 6, 11, 16.

3 0

3 years ago

Read 2 more answers

I need help please!!

guajiro [1.7K]

13-11 = 2

15-13 = 2

17-15 = 2

As you can see, the numbers increased by two. hence the answer is 2.

5 0

3 years ago

A study by a reputable research organization found that when presented with prints from the same individual, a fingerprint expe

Llana [10]

Answer:

a. 0.6899

b. 0.1642

Step-by-step explanation:

a. Given the probability of success is 0.94 for an expert and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of the events is calculated as:

$P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.94\times0.94\times0.94\times0.94\times0.94\times0.94\\\\=0.6899$

Hence, the probability of correctly identifying the 6 matches is 0.6899

b.Given the probability of success is 0.74 for a novice and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of the events is calculated as:

$P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.74\times0.74\times0.74\times0.74\times0.74\times0.74\\\\=0.1642$

#Hence, the probability of correctly identifying the 6 matches is 0.1642

*I have used the sample size of 6(due to conflicting info/question size).

7 0

4 years ago

Previously, an organization reported that teenagers spent 24.5 hours per week, on average, on the phone. The organization thinks

Lena [83]

Answer:

We need to develop a one-tail t-student test ( test to the right )

We reject H₀ we find evidence that student spent more than 24,5 hours on the phone

Step-by-step explanation:

Sample size n = 15 n < 30

And we were asked if the mean is higher than, therefore is a one-tail t-student test ( test to the right )

Population mean μ₀ = 24,5

Sample mean μ = 25,7

Sample standard deviation s = 2

Hypothesis Test:

Null Hypothesis H₀ μ = μ₀

Alternative Hypothesis Hₐ μ > μ₀

t (c) = ?

We will define CI = 95 % then α = 5 % α = 0,05 α/2 = 0,025

n = 15 then degree of freedom df = 14

From t-student table we get: t(c) = 2,1448

And t(s)

t(s) = ( μ - μ₀ ) / s/√n

t(s) = (25,7 - 24,5) /2/√15

t(s) = 2,3237

Now we compare t(c) and t(s)

t(c) = 2,1448 t(s) = 2,3237

t(s) > t(c)

Then we are in the rejection region we reject H₀ we have evidence at 95% of CI that students spend more than 24,5 hours per week on the phone

8 0

3 years ago

Factor the expression using the GCF.<br><br> 14x−98

pashok25 [27]

Answer: 14(x−7)

Hope this helps :)

8 0

3 years ago

Read 2 more answers

Resolve in factors. I) x⁴+x²+1​

Resolve in factors. I) x⁴+x²+1