1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PolarNik [594]
3 years ago
14

Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. Which statement describes the number and nature of

all roots for this function?
Chemistry
2 answers:
Daniel [21]3 years ago
3 0
The two roots of this functions are the exact roots and one is an imaginary root. The -2 is the root of a negative number -16 because if you compute the -2 on its 3rd power you come up -16, the 2 is the root of 16 and the 4+i contains a imaginary number that is why it is an imaginary root
slava [35]3 years ago
3 0

Answer:

f(x) has three real roots and two imaginary roots.

Explanation:

It is given that the three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. In which -2,2 are real root and 4+i is imaginary root.

The number of roots of a polynomial is equal to the degree of that polynomial.

Since the degree of polynomial function is 5, therefore the function has total 5 roots.

According to the complex conjugate root theorem, if a+ib is a root of a polynomial, then its conjugate a-ib is also a root of that function. The number of imaginary roots are always an even number.

Since 4+i is a root of the polynomial, therefore 4-i is also a root of the function.

2 roots are real and 2 roots are imaginary. The remaining 1 root must be real because the number of imaginary roots can not be odd.

Therefore the function f(x) has three real roots and two imaginary roots.

You might be interested in
What is the Big Bang
Mnenie [13.5K]
<span>the rapid expansion of matter from a state of extremely high density and temperature that according to current cosmological theories marked the origin of the universe.</span>
7 0
3 years ago
How do strong southerly winds affect the vapor pressure?
dedylja [7]

Answer:

An increase

Explanation:

The strong southerly winds affect the vapor pressure by increasing it .

When the vapor pressure increases it means an increase in temperature and more evaporation occurs.

A decrease in the vapor pressure means a reduction in temperature with less amount of evaporation being involved

5 0
3 years ago
If you have a balloon inside a car at noon during a hot summer day, the balloon molecules
aleksandrvk [35]

Answer:

it decreases

Explanation:

because its false

6 0
3 years ago
Read 2 more answers
If you have access to stock solutions of 1.00 M H3PO4, 1.00 M of HCl, and 1.00 M NaOH solution, (and distilled water of course),
garri49 [273]

Answer:

0.10L of 1.00M of H₃PO₄ and 0.1613L of 1.00M NaOH

Explanation:

The pKa's of phosphoric acid are:

H₃PO₄/H₂PO₄⁻ = 2.1

H₂PO₄⁻/HPO₄²⁻ = 7.2

HPO₄²⁻/PO₄³⁻ = 12.0

To make a buffer with pH 9.40 we need to convert all H₃PO₄ to H₂PO₄⁻ and an amount of H₂PO₄⁻ to HPO₄²⁻

To have a 50mM solution of phosphoures we need:

2L * (0.050mol / L) = 0.10 moles of H₃PO₄

0.10 mol * (1L / mol) = 0.10L of 1.00M of H3PO4

To convert the H₃PO₄ to H₂PO₄⁻ and to HPO₄²⁻ must be added NaOH, thus:

H₃PO₄ + NaOH → H₂PO₄⁻ + H₂O + Na⁺

H₂PO₄⁻ + NaOH → HPO₄²⁻ + H₂O + Na⁺

Using H-H equation we can find the amount of NaOH added:

pH = pKa + log [A⁻] / [HA] <em>(1)</em>

<em>Where [A-] is conjugate base, HPO₄²⁻ and [HA] is weak acid, H₂PO₄⁻</em>

<em>pH = 7.40</em>

<em>pKa = 7.20</em>

[A-] + [HA] = 0.10moles <em>(2)</em>

Replacing (2) in (1):

7.40 = 7.20 + log 0.10mol - [HA] / [HA]

0.2 = log 0.10mol - [HA] / [HA]

1.5849 = 0.10mol - [HA] / [HA]

1.5849 [HA] = 0.10mol - [HA]

2.5849[HA] = 0.10mol

[HA] = 0.0387 moles = H₂PO₄⁻ moles

That means moles of HPO₄²⁻ are 0.10mol - 0.0387moles = 0.0613 moles

The moles of NaOH needed to convert all H₃PO₄ in H₂PO₄⁻ are 0.10 moles

And moles needed to obtain 0.0613 moles of HPO₄²⁻ are 0.0613 moles

Total moles of NaOH are 0.1613moles * (1L / 1mol) = 0.1613L of 1.00M NaOH

Then, you need to dilute both solutions to 2.00L with distilled water.

4 0
3 years ago
1. Find the molar mass of the compounds<br>a. K2Cro4​
Luda [366]

Answer:

194.1903

Explanation:

that is for one mole of K2Cro4

8 0
3 years ago
Other questions:
  • Whats the ph for a solution poh4 9.78 concentration of solution
    10·1 answer
  • Combustion analysis of toluene, a common organic solvent, gives 8.20 mg of co2 and 1.92 mg of h2o. if the compound contains only
    11·1 answer
  • (1.8 x 10-2) ÷ (9 x 102) =
    9·2 answers
  • 9. Given the following reaction:CO (g) + 2 H2(g) CH3OH (g)In an experiment, 0.45 mol of CO and 0.57 mol of H2 were placed in a 1
    9·1 answer
  • On a hot summer day in Florida, Sarah was having a picnic with her family. She took a glass, which had been sitting in the Sun,
    6·1 answer
  • HELPPPPPPP!!!!!!!!!!
    13·2 answers
  • Scientists classify organisms into three domains and six kingdoms. In which
    9·1 answer
  • Hdjshjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj???????????????
    6·1 answer
  • One app named meet here is the link of that come here with the link<br><br><br>stnjgsozbq​
    14·1 answer
  • Rev
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!