WorksheetsRational Root Theorem Zeros to Functions Descartes Rule of Signs
Total questions: 20
Worksheet time: 20mins
According to Descartes' Rule of Signs, how can you determine the number of possible positive real roots of a polynomial?
By counting the number of sign changes in the polynomial’s coefficients
By solving the polynomial for x=0
By factoring the polynomial into linear factors
By analyzing the degree of the polynomial
Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x3 + 2x2 - 6x + 8
±1, ±8
±1, ±2, ±4, ±8
±1, ±2, ±4
1, 2, 4, 8
Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x3 + 2x2 - 6x + 7
±1, ±7, ±1/3, ±7/3
±1, 7
±1, ±3, ±7, ±7/3
±1, ±3, ±7, ±1/3, ±7/3
Solve by using Rational Root Theorem:
x3 - 7x - 6 = 0
1, 2, 3
-1, -2, - 3
-1, -2, 3
1,-2,-3
List all the possible rational zeros
h(x) = x3 - 5x2+2x+12
1,2,3,4,6,12
1,2,6,12
1,2,3,4,6,12,-1,-2,-3,-4,-6,-12
List all possible rational zeros
f(x) = 3x5-5x2+x+6
1, 2, 3, 6, -1, -2, -3, -6
1/3,2/3,1,2,3,6,-1/3,-2/3,-1,-2,-3,-6
1/3,2/3,1,2,3,6
List all possible rational zeros
f(x) = 3x5-5x2+x+6
±1, ±2, ±3, ±6
±1/3, ±2/3, ±1, ±2, ±3, ±6
±1/3, ±2/3, ±1, ±2, ±3, ±6
List all of the possible rational zeros
p(x) = 3x2+x+7
-1/3, -7/3, -1, -7, 1/3,7/3,1,7
1/3,7/3,1,7
1, 7, 14, 21
Which of the following is a COMPLETE list of all possible Rational Zeros? f(x) = x3 + 2x2 - 6x + 8
±1, ±8
±1, ±2, ±4, ±8
±1, ±2, ±4
1, 2, 4, 8
Find all of the rational zeros of each function.
q(x) = x3+3x2-6x-8
1, 2, 4, 8, -1, -2, -4, -8
-4, -1, 2
1, 2, 4
Use Descartes Rule of Signs to determine the possible number of positive and negative roots.
3 or 1 positive roots and 0 negative roots
4, 2, or 0 positive roots and 1 negative root
4, 2, or 0 positive roots and 0 negative roots
2 or 0 positive roots and 1 negative roots
Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x3 + 5x2 - 9x + 5
±1, ±5, ±1/2, ±5/2
±1, ±2, ±5, ±1/2, ±5/2
±1, ±5
±1, ±2, ±5, ±1/2, ±5/2, ±2/5
Solve by using Rational Root Theorem:
2x3 - 11x2 + 12x + 9 = 0
-1, 1, 3
-1, 3/2, 3
-1/2, 3, 3
-1/2, 1, 3
According to the Rational Root Theorem, what are the all possible rational roots?
2x3 - 11x2 + 12x + 9 = 0
±1,±2
±1,±3,±9
±1,±3±9,±1/2,±3/2,±9/2
±1,±2,±1/3,±2/3,±1/9,±2/9
Below are four possible zeros for this polynomial.
Figure out which one "works"
f(x) = x3 + 2x2 - 11x - 12
-3
-4
1
6
Below are four possible zeros for this polynomial. Figure out which one "works" f(x) = x3 - 8x2 - 23x + 30
3
-1
-10
1
How many possible negatives solutions does the following polynomial have? f(x) = x4 - 3x3 - 17x2 + 39x -20
3 or 1
3
1
2 or 0
Use Descartes Rule of Signs to determine the possible number of positive and negative roots.
1 positive, 2 or 0 negative
1 positive, 1 negative
0 positive, 1 negative
1 positive, 0 negative
Find the zeros of the polynomial given one factor. Use synthetic division.
X= 3,4,5
x=-3,-4,-5
x=-3,4,5
x= 3, -4, -5
Using Descartes' Rule of Signs, how many possible NEGATIVE roots are there for the polynomial f(x) = x4+x3+x2+x+5. Select all that apply.
0
1
2
3
4
