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Rational roots and Descartes rule
Rational roots and Descartes rule
ans:
syntax error
C
DEL
ANS
±
(
)
÷
×
7
8
9
–
4
5
6
+
1
2
3
=
0
.
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Question 1:
1 pts
x
=
3
x = 3
x
=
3
is a possible rational root of polynomial
p
(
x
)
=
x
5
+
3
x
4
−
8.
p(x)=x^5+3x^4-8.
p
(
x
)
=
x
5
+
3
x
4
−
8.
Question 2:
1 pts
Which one of these is not possible real zero of
p
(
x
)
=
2
x
3
+
x
2
−
7
x
−
1
p(x) = 2x^3 + x^2 - 7x -1
p
(
x
)
=
2
x
3
+
x
2
−
7
x
−
1
:
1
1
2
\frac{1}{2}
2
1
2
−
1
2
-\frac12
−
2
1
Question 3:
2 pts
All possible rational roots of the polynomial
p
(
x
)
=
2
x
5
−
x
2
+
3
p(x)=2x^5-x^2+3
p
(
x
)
=
2
x
5
−
x
2
+
3
are
±
3
±
1
±
3
2
\pm 3 \pm1 \pm \frac32
±
3
±
1
±
2
3
±
3
±
1
±
2
3
\pm3 \pm1 \pm \frac{2}{3}
±
3
±
1
±
3
2
±
1
3
±
1
±
2
3
\pm\frac{1}{3}\pm1 \pm\frac{2}{3}
±
3
1
±
1
±
3
2
±
1
3
±
1
±
3
2
\pm\frac{1}{3} \pm1 \pm\frac{3}{2}
±
3
1
±
1
±
2
3
Question 4:
2 pts
All possible rational roots of the polynomial
p
(
x
)
=
4
x
5
−
x
2
+
1
p(x)=4x^5-x^2+1
p
(
x
)
=
4
x
5
−
x
2
+
1
are
±
1
±
2
±
4
\pm1 \pm2 \pm4
±
1
±
2
±
4
±
1
±
4
\pm1 \pm4
±
1
±
4
±
1
±
2
±
1
4
\pm1 \pm2 \pm\frac{1}{4}
±
1
±
2
±
4
1
±
1
±
1
2
±
1
4
\pm1 \pm\frac{1}{2} \pm \frac{1}{4}
±
1
±
2
1
±
4
1
Question 5:
2 pts
Usig a rational root test we can find all roots of the polynomial.
Question 6:
2 pts
x
=
2
x= \sqrt{2}
x
=
2
is a rational root of
p
(
x
)
=
x
2
−
2
p(x)=x^2-2
p
(
x
)
=
x
2
−
2
Question 7:
2 pts
how many sign changes has polynomial
p
(
x
)
=
x
3
+
x
2
+
x
−
1
p(x)=x^3+x^2+x-1
p
(
x
)
=
x
3
+
x
2
+
x
−
1
.
0
0
0
1
1
1
2
2
2
3
3
3
Question 8:
2 pts
What is the sequence of pairs of successive signs for the polynomial
p
(
x
)
=
x
3
−
x
2
+
x
−
3
p(x)=x^3-x^2+x-3
p
(
x
)
=
x
3
−
x
2
+
x
−
3
- + -
- + - +
+ + - -
+ - + -
Question 9:
3 pts
What is the maximum number of positive zeroes for the polynomial
p
(
x
)
=
−
x
4
−
x
3
+
x
2
−
1
p(x) =-x^4-x^3+ x^2-1
p
(
x
)
=
−
x
4
−
x
3
+
x
2
−
1
4
4
4
3
3
3
2
2
2
1
1
1
Question 10:
3 pts
What is the number of negative zeroes for the polynomial
p
(
x
)
=
x
6
−
x
5
+
2
x
3
−
4
x
2
−
1
p(x) =x^6-x^5+2x^3-4x^2-1
p
(
x
)
=
x
6
−
x
5
+
2
x
3
−
4
x
2
−
1
4
4
4
3
3
3
2
2
2
1
1
1
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Pre-algebra
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Trigonometry
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Basics of polynomials
Definition, degree and names
Evaluating polynomials
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Combining like terms
Adding and subtracting
Multiplying polynomials
Division and Remainder theorem
Roots of polynomials
Properties of polynomial roots
Rational roots and Descartes Rule
Factoring Polynomials
Factoring out a common factor
Factoring by grouping
Difference between two squares
Perfect square trinomial
Greatest common factor
Factoring trinomials
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Identifying polynomials graph
Transformations of polynomial functions
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