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Category: Math Homework
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Experience:  B.S. in Civil Engineering
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# Any answers & explanations would be much appreciated!! Which

### Resolved Question:

Any answers & explanations would be much appreciated!!

Which of these is the result of (x^5-x^3+2x^2-9x+5)/(x+2)?
a. x^4+2x^3+3x^2+8x-1+ (3/x+2)
b. x^3-3x^2+8x-25+ (25/x+2)
c. x^4-2x^3+3x^2-4x-1+ (7/x+2)
d. x^3+x^2+4x-1+ (3/x+2)

Evaluate log 1/4 1/16
a. 1/2
b. 1/4
c. 2
d. 4

which of these is the remainder when 4x^4-5x^3+9 is divided by x-3?
a. (468)/(4x^4-5x^3+9)
b. (198)/(x-3)
c. (468)/(x-3)
d. (198)/(4x^4-5x^3+9)

which of these is a factor of 2x^100-x^7-1?
a. x-1
b. x
c. x+1
d. x-2

which are upper and lower bounds for the real roots of 3x^4-2x^3+x-9=0?
a. 0 and 3
b. -2 and 2
c. -3 and -1, 1, and 3
d. -2 and -1, 1, and 2

is it possible for a degree-4 polynomial P(x) to have only complex (no real) roots?
a. no it is not possible
b. yes, but neither the coefficients P(x) nor those of p(-x) can have any signs
c. yes, but the coefficients must have no sign changes, althougth the coeff of p(-x) may have no sign changes
d. yes but the coefficients of p(x) must have 4 sign changes

if 2-i is a root of 3x^3-11x+5, then what are it's other roots?
a. 2+i and 5/3
b 2+ i and 0
c -5, -5/3, -1, -1/3, 1/3, 1, 5/3, 5
d. 2+i and -1/3

which is better for the investor, an investment that pays 2% annual interest compounded monthly or an investment that pays 2.1% interest annually?
a. the 2.1% annual is better
b. the 2% with monthly compound is better
c. you cannot compare plans with different frequencies of compounding
d. the two plans are equal

if 1 and -6 are two of the roots of 6x^4+31x^3-33x^2-16x+12, then what are the other two?
a. 2 and 3/2
b. 1/2 and -2/3
c. -1 and 6
d. -2 and 2/3

if p(x) is a polynomial with P(-6)=-1.12 and P(-5)=0.6 then which of the following must be true?
a. there is a zero for p(x) between x=-6 and x=-5 but it may be a complex number
b there is a zero for p(x) between x=-6 and x=-5
c.there is a zero for p(x) between x=-1.12 and x=-.6
there is a zero for p(x) between x=-1.12 and x=-.6 but it may be a complex number

what would a graph of y=e^x+1 look like?

use the rational roots theorem to list all possible rational roots of 24x^3+2x-7

solve ln t=log 50 for t
a. t= 50
b. t=13.6
c. t= 8166.3
d. t= 5.47

if a cubic polynomial has roots -5 and 6-2i, what is its third root?
a. -30+10i
b. 5
c. 6+2i
d. 1-2i

find the negative root of x^2-3=0 to the nearest tenth
a. -1.4
b. -1.7
c. 1.7
d. 1.4

find all roots of x^3+2x^2+2x+1. hint: find the rational one(s) first
a. -1, -1/2 -1/2 sqrt3, -1/3+1/2sqrt3
b. 1, 2, -2
c. -1, -1/2-1/2isqrt3, -1/2+1/2isqrt3
d. -1, 1/2, -1/2

how many roots does x^6 =3x^5+1 have?
a. 1
b. 11
c. 6
d. 5
Submitted: 3 months ago.
Category: Math Homework
Expert:  Ryan replied 3 months ago.
Hi,

Thank you for your questions. I'll be happy to help you with these. It will take some time to write up explanations for these, but I'll have them posted for you as soon as possible.

Thanks,

Ryan
Customer: replied 3 months ago.

Ok thanks... I was just hoping to see some explanation to help me understand.. I'm having a hard time with this last chapter.

Expert:  Ryan replied 3 months ago.
Hi Jenn,

You're welcome. I'm working on them now. I'll try to include as much explanation as seems needed, and you can always ask for further information if necessary. I'll be happy to explain anything that is not clear.

Ryan
Expert:  Ryan replied 3 months ago.
Hi Jenn,

Here are the solutions:

Solutions

Note: There was one problem where none of the answer choices was correct. This is noted in the solution file at the above link. Please check the problem for any typing errors. I'll be happy to revisit the problem if needed.

Thanks,

Ryan
Customer: replied 3 months ago.

Thank you so much, I will review the answers shortly.

I did take note to the equation you mentioned may have been incorrect... and it was, I missed a part of the equation (see below)

wrong equation: if 2-i is a root of 3x^3-11x+5, then what are it's other roots?

corrected equation: if 2-i is a root of 3x^3-11x^2+11x+5, then what are it's other roots?
a. 2+i and 5/3
b 2+ i and 0
c -5, -5/3, -1, -1/3, 1/3, 1, 5/3, 5
d. 2+i and -1/3

Expert:  Ryan replied 3 months ago.
Hi Jenn,

Thank you for corrected equation.

If 2 - i is a root, then 2 + i is also a root, because complex roots are always present in pairs, with each root being the complex conjugate of the other.

The two complex roots lead to factors of (x - 2 - i) and (x - 2 + i). Multiplying these two roots together gives:

(x - 2 - i)(x - 2 + i) = x^2 - 2x + ix - 2x + 4 - 2i - ix + 2i - i^2 = x^2 - 4x + 5

Using polynomial long division to divide 3x^3 - 11x^2 + 11x + 5 by x^2 - 4x + 5 gives the result of 3x + 1. This is the last factor of the polynomial expression.

Setting this factor equal to zero and solving for x gives:

3x + 1 = 0

3x = -1

x = -1/3

The roots are then 2 - i, 2 + i, and -1/3

Therefore, the "other" roots are 2 + i and -1/3

Solution: D. 2+i and -1/3

Thanks,

Ryan
Ryan, Engineer
Category: Math Homework
Satisfied Customers: 6912
Experience: B.S. in Civil Engineering

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