Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 2
Fundamental Theorem of Algebra
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
5
−
12
x
4
−
20
x^5 - 12x^4 - 20
x
5
−
12
x
4
−
20
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
5
x
4
+
11
x
3
−
9
x
2
+
8
x
−
8
5x^4 + 11x^3 - 9x^2 + 8x - 8
5
x
4
+
11
x
3
−
9
x
2
+
8
x
−
8
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
6
x
5
−
9
x
3
+
7
6x^5 - 9x^3 + 7
6
x
5
−
9
x
3
+
7
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
−
6
x
3
−
17
x
−
13
-6x^3 - 17x - 13
−
6
x
3
−
17
x
−
13
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
6
x
4
+
8
x
3
−
12
x
2
−
10
x
+
20
6x^4 + 8x^3 - 12x^2 - 10x + 20
6
x
4
+
8
x
3
−
12
x
2
−
10
x
+
20
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
6
+
x
4
−
12
x
3
+
17
x
2
−
9
x
+
15
x^6 + x^4 - 12x^3 + 17x^2 - 9x + 15
x
6
+
x
4
−
12
x
3
+
17
x
2
−
9
x
+
15
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
4
+
20
x
−
18
x^4 + 20x - 18
x
4
+
20
x
−
18
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
4
x
5
+
3
x
4
−
2
x
3
−
10
x
2
−
18
x
−
10
4x^5 + 3x^4 - 2x^3 - 10x^2 - 18x - 10
4
x
5
+
3
x
4
−
2
x
3
−
10
x
2
−
18
x
−
10
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
−
2
x
4
+
17
x
3
+
12
x
2
−
3
-2x^4 + 17x^3 + 12x^2 - 3
−
2
x
4
+
17
x
3
+
12
x
2
−
3
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
6
x
5
+
18
x
3
−
9
x
2
+
19
6x^5 + 18x^3 - 9x^2 + 19
6
x
5
+
18
x
3
−
9
x
2
+
19
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
8
x
4
+
8
8x^4 + 8
8
x
4
+
8
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
−
2
x
4
+
13
-2x^4 + 13
−
2
x
4
+
13
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
6
−
20
x
5
−
6
x
4
+
16
x^6 - 20x^5 - 6x^4 + 16
x
6
−
20
x
5
−
6
x
4
+
16
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
6
+
14
x
5
−
10
x
4
−
16
x
3
+
x
2
−
6
x
+
4
x^6 + 14x^5 - 10x^4 - 16x^3 + x^2 - 6x + 4
x
6
+
14
x
5
−
10
x
4
−
16
x
3
+
x
2
−
6
x
+
4
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
−
3
x
3
−
19
x
2
+
18
-3x^3 - 19x^2 + 18
−
3
x
3
−
19
x
2
+
18
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
6
+
15
x
5
+
7
x
4
−
18
x
3
−
5
x
2
+
17
x
+
6
x^6 + 15x^5 + 7x^4 - 18x^3 - 5x^2 + 17x + 6
x
6
+
15
x
5
+
7
x
4
−
18
x
3
−
5
x
2
+
17
x
+
6
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
6
−
17
x
5
+
19
x
4
+
18
x
3
−
11
x
2
+
16
x
−
16
x^6 - 17x^5 + 19x^4 + 18x^3 - 11x^2 + 16x - 16
x
6
−
17
x
5
+
19
x
4
+
18
x
3
−
11
x
2
+
16
x
−
16
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
3
+
4
x
2
+
11
x^3 + 4x^2 + 11
x
3
+
4
x
2
+
11
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
4
x
3
+
13
x
2
+
13
x
+
13
4x^3 + 13x^2 + 13x + 13
4
x
3
+
13
x
2
+
13
x
+
13
\newline
____
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
x
6
+
x
5
+
3
x
2
−
x
+
15
x^6 +x^5 + 3x^2 - x + 15
x
6
+
x
5
+
3
x
2
−
x
+
15
\newline
____
Get tutor help
A polynomial
p
p
p
has zeros when
x
=
1
5
,
x
=
−
4
x=\frac{1}{5}, x=-4
x
=
5
1
,
x
=
−
4
, and
x
=
2
x=2
x
=
2
.
\newline
What could be the equation of
p
p
p
?
\newline
Choose
1
1
1
answer:
\newline
(A)
p
(
x
)
=
(
1
5
x
)
(
−
4
x
)
(
2
x
)
p(x)=\left(\frac{1}{5} x\right)(-4 x)(2 x)
p
(
x
)
=
(
5
1
x
)
(
−
4
x
)
(
2
x
)
\newline
(B)
p
(
x
)
=
(
−
1
5
x
)
(
4
x
)
(
−
2
x
)
p(x)=\left(-\frac{1}{5} x\right)(4 x)(-2 x)
p
(
x
)
=
(
−
5
1
x
)
(
4
x
)
(
−
2
x
)
\newline
(C)
p
(
x
)
=
(
5
x
+
1
)
(
x
−
4
)
(
x
+
2
)
p(x)=(5 x+1)(x-4)(x+2)
p
(
x
)
=
(
5
x
+
1
)
(
x
−
4
)
(
x
+
2
)
\newline
(D)
p
(
x
)
=
(
5
x
−
1
)
(
x
+
4
)
(
x
−
2
)
p(x)=(5 x-1)(x+4)(x-2)
p
(
x
)
=
(
5
x
−
1
)
(
x
+
4
)
(
x
−
2
)
Get tutor help
Consider the complex number
\newline
z
=
−
7
2
2
−
7
2
2
i
z=-\frac{7 \sqrt{2}}{2}-\frac{7 \sqrt{2}}{2} i \text { }
z
=
−
2
7
2
−
2
7
2
i
\newline
Which of the following complex numbers best approximates
z
3
z^{3}
z
3
? Hint:
z
z
z
has a modulus of
7
7
7
and an argument of
22
5
∘
225^{\circ}
22
5
∘
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
14.8
−
14.8
i
-14.8-14.8 i
−
14.8
−
14.8
i
\newline
(B)
242.5
−
242.5
i
242.5-242.5 i
242.5
−
242.5
i
\newline
(C)
−
21
-21
−
21
\newline
(D)
343
i
343 i
343
i
Get tutor help
Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.
\newline
8
x
3
−
5
x
2
−
9
8x^3 - 5x^2 - 9
8
x
3
−
5
x
2
−
9
\newline
______
Get tutor help
