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Svet_ta [14]
3 years ago
6

For the function y=x^5+1x^3-30x, find all real zeros.

Mathematics
1 answer:
siniylev [52]3 years ago
4 0

Answer:

The real zeroes are -√5 , 0 , √5

Step-by-step explanation:

* Lets explain how to solve the problem

- The function is y = x^5 + x³ - 30x

- Zeros of any equation is the values of x when y = 0

- To find the zeroes of the function equate y by zero

∴ x^5 + x³ - 30x = 0

- To solve this equation factorize it

∵ x^5 + x³ - 30x = 0

- There is a common factor x in all the terms of the equation

- Take x as a common factor from each term and divide the terms by x

∴ x(x^5/x + x³/x - 30x/x) = 0

∴ x(x^4 + x² - 30) = 0

- Equate x by 0 and (x^4 + x² - 30) by 0

∴ x = 0

∴ (x^4 + x² - 30) = 0

* Now lets factorize (x^4 + x² - 30)

- Let <em>x² = h</em> and <em>x^4 = h²</em> and replace x by h in the equation

∴ (x^4 + x² - 30) = (h² + h - 30)

∵ (x^4 + x² - 30) = 0

∴ (h² + h - 30) = 0

- Factorize the trinomial into two brackets

- In trinomial h² + h - 30, the last term is negative then the brackets

 have different signs (     +     )(     -     )

∵ h² = h × h ⇒ the 1st terms in the two brackets

∵ 30 = 5 × 6 ⇒ the second terms of the brackets

∵ h × 6 = 6h

∵ h × 5 = 5h

∵ 6h - 5h = h ⇒ the middle term in the trinomial, then 6 will be with

  (+ ve) and 5 will be with (- ve)

∴ h² + h - 30 = (h + 6)(h - 5)

- Lets find the values of h

∵ h² + h - 30 = 0

∴ (h + 6)(h - 5) = 0

∵ h + 6 = 0 ⇒ subtract 6 from both sides

∴ h = -6

∵ h - 5 = 0 ⇒ add 5 to both sides

∴ h = 5

* Lets replace h by x

∵ <em>h = x²</em>

∴ x² = -6 and x² = 5

∵ x² = -6 has no value (<em>no square root for negative values</em>)

∵ x² = 5 ⇒ take √ for both sides

∴ x = ± √5

- There are three values of x ⇒ x = 0 , x = √5 , x = -√5

∴ The real zeroes are -√5 , 0 , √5

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Answer: Less than $100,831

Step-by-step explanation:

There is an equation for the calculation monthly payment which is:

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x = 155,000 × 0.00367 × (1.00367^240) / (1.00367^240) - 1

x = $972.27

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$973.3 × 240 = $233,352

Therefore, the total amount, which is the loan plus the interest, will be 233,352 dollars.

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3 years ago
What single decimal multiplier would you use to increase by 9% followed by 3% decrease
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Answer:

= 94

Step-by-step explanation:

To work out the multiplier, first add or subtract the percentage from 100, then convert to a decimal. Example: we want to add 20% to £110. To work out the multiplier, add 20 to 100, to get 120, and then change it to a decimal (divide by 100) to get 1.2. The answer is £110 x 1.2 = £132.

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Step-by-step explanation:

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2 years ago
Approximately 40% of the calls to an airline reservation phone line result in a reservation being made. (round to three decimal
IRISSAK [1]

Answer:

The probability that none of the 10 calls result in a reservation is 0.60%.  In turn, the probability that at least one call results in a reservation being made is 99.40%.

Step-by-step explanation:

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3 0
2 years ago
What is (+5) - (-1) - (-3)
maksim [4K]
+ = positive
Positive and positive makes a positive

Negative and negative makes a positive

- = negative
Negative and positive makes a negative

Positive and negative makes a negative

Your answer: +5 - (-1) = 6
+6 - (-3) = +9
Your answer that youre looking for is: 9


4 0
3 years ago
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