The leading term text

[Soso]

Can any explain to me how I can solve this problem please?

write one polynomial p(x) of a degree 7 which satisfies all of (a)-(f):

a) P(x) tends to negative infinity as x tends to positive infinity
b) P(x) tends to positive infinity as x tends to negative infinity
c) p(x) has a zero at x = -1 of multiplicity 3
d) p(x) has a zero at x = 0 of multiplicity 2;
e) p(x) has a zero at x =

of multiplicity 1
f) P(x) has a zero at x = 15/2 of multiplicity 1

 

[Steven G]

Can any explain to me how I can solve this problem please?

write one polynomial p(x) of a degree 7 which satisfies all of (a)-(f):

a) P(x) tends to negative infinity as x tends to positive infinity
b) P(x) tends to positive infinity as x tends to negative infinity
c) p(x) has a zero at x = -1 of multiplicity 3
d) p(x) has a zero at x = 0 of multiplicity 2;
e) p(x) has a zero at x =

of multiplicity 1
f) P(x) has a zero at x = 15/2 of multiplicity 1

What have you tried?
a) the coefficient of the leading term must be neg
b) 7th degree and part a is enough
c-f is most obvious

 

[Soso]

What have you tried?
a) the coefficient of the leading term must be neg
b) 7th degree and part a is enough
c-f is most obvious

Thank you for your help

I have just answered those question and I got the following but I am not sure whether I am correct.

b) 7 degree with negative coefficient
c) (x+1)^3
d) x^2
e) (x-

) I am really confused at this one
f) (x-15/2)

 

[Steven G]

Thank you for your help

I have just answered those question and I got the following but I am not sure whether I am correct.

b) 7 degree with negative coefficient
c) (x+1)^3
d) x^2
e) (x-

) I am really confused at this one
f) (x-15/2)

I think that you do not understand the question. There are not six questions a-f. There is one question and that question is to find the equation a polynomial which has the properties a-f. So what is the equation of the polynomial? pi is just a number like 2, sqrt(7), e^3 and [sqrt(3)]^(sqrt(7))

 

[Soso]

I think that you do not understand the question. There are not six questions a-f. There is one question and that question is to find the equation a polynomial which has the properties a-f. So what is the equation of the polynomial? pi is just a number like 2, sqrt(7), e^3 and [sqrt(3)]^(sqrt(7))

I do not know. I am really confused. Do you mean like this?

P(x)= -x^2(x+1)^2(x+

)(x-15/2)

 

[Steven G]

I do not know. I am really confused. Do you mean like this?

P(x)= -x^2(x+1)^2(x+

)(x-15/2)

Yes, that is a polynomial. Can you now write a polynomial that has the properties a-f. Also stop using a picture for pi, just write pi!

 

[Soso]

Yes, that is a polynomial. Can you now write a polynomial that has the properties a-f. Also stop using a picture for pi, just write pi!

I really have no idea about this. I do not know how I can do it

 

[stapel]

I really have no idea about this. I do not know how I can do it

Okay. Which are the terms, etc, in which parts of the exercise that you don't understand? For instance, are you needing lesson instruction on what "zeroes" are? What "multiplicities" are? What "tends" means in this context? And so forth.

We'll be glad to try to find links for online lessons, so you can learn the underlying material, but it would be helpful to have some direction. Please be specific and complete. Thank you!

 

[Steven G]

You answered a-f correctly. Now all you need to do is multiply the factors together.

p(x)= -7(x+1)^3 (x^2)(x-pi)(x-15/2). The -7 could have been any negative number.

If you have any questions about why this works or anything else about this problem then let us know.