Find the polynomial f(x) of degree three that has zeroes at 1, 2, and
4 such that f(0) = -16.
a. f (x) = x3 − 7x2 +14x −16
b . f (x) = 2x3 −14x 2 + 28x −16
c . f (x) = 2x3 −14x 2 +14x −16
d . f (x) = 2x3 + 7x2 +14x +16

Find the third degree polynomial whose graph is shown in the figure.

a. f (x) = x3 −x 2 −2x + 2
b . 2
2
1
4
f (x) = 1 x3 − x 2 −x +
c . 2 2
4
1
4
f (x) = 1 x3 − x 2 + x +
d . 2
2
1
2
f (x) = 1 x3 + x 2 −x +

The figure shows the graph of the polynomial function y = f(x). For
which of the values k = 0, 1, 2, or 3 will the equation f(x) = k have
complex roots?
a. 0
b . 1
c . 2
d . 3

Polynomials, zeros and complex roots are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

1. Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
F(x)=x^5-x^4+7x^3-8x^2-16x+13; [1.3,1.7]
Find value of f (1.3) ____ (simplify)
Find value of f (1.7) ______ (simplify)
2. Information is given about the polynomial f(x) whose coefficients a

1. Form a polynomial f(x) with real coefficents having the given degree andzeros
Degree 5; Zeros: 2; -i; -7+i
Enter the polynomial f(x)=a(____) type expression using x as the variable.
2. Find a bound on the real zeros of the polynomial function.
F(x)=x^4+x^3-4x-6
Every real zero of f lies between -____and ____ (its not

Show that if the roots of the polynomial p are all real, then the roots of p' are all real. If, in addition, the roots of p are all simple, then the roots of p' are all simple.

1) Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. If a zero has multiplicity greater than one, only enter the root once.)
P(x) = x^3 â?' 6x^2 + 11x â?' 6
x=
Write the polynomial in factored form.
P(x) =
2) Find all rational zeros of the polynomial. (Enter your answers as a c

1) A polynomial P is given.
P(x) = x^4 + 49x^2
(a) Find all zeros of P, real andcomplex. (Enter your answers as a comma-separated list. If a root has multiplicity greater than one, only enter the root once.)
x =
(b) Factor P completely.
P(x) =
2) A polynomial P is given.
P(x) = x^3 â?' 10x^2 + 50x
(a) Find all zer

Determine whether the polynomials have multiple roots.
See attached file for full problem description.
19. Let F be a field and let f(x) =...... The derivative, D(f(x)), of f(x) is defined by
D(f(x)) = ......
where, as usual, ....... (n times). Note that D(f(x)) is again a polynomial with coefficients in F.
The polynomi

Question 1) Determine whether the function is a polynomial function. If it is, state the degree. If it is not, tell why not.
G(x)=7(x-5)^2(x^2+6)
a) Polynomial of degree 4
b) Polynomial of degree 7
Question 2) Form a polynomial whose real zerosand degree are given. Zeros: -1, 0, 5. Degree: 3
Write a polynomial with in

Determine if the following have a solution or not? justify answer.
(apply the discriminant) are the roots real, repeated real, or complex?
1) 5x^2+8x+7=0
2) (7)^1/2y^2-6y-13(7)^1/2=0
3) 2x^2=x-1=0
4) 4/3x^2-2x+3/4=0
5) 2x^2+5x+5=0
6) p^2-4p+4=0
7) m^2=m+1=0
8) 3z^2+z-1=0

1) Factor the polynomial completely.
P(x) = x^2 + 9
P(x) =
Find all its zeros. State the multiplicity of each zero. (If an answer does not exist, enter DNE.)
real zero x=______ with multiplicity______
complex zero x=_______(positive imaginary part) with multiplicity ____
co