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Precalculus: 3.4
Precalculus: 3.4
15
Mathematics
Undergraduate 1
10/19/2015

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Cards

Term
What Are The Objectives of 3.4?
Definition
-Review Real Zeroes of Polynomials
-Use Rational Zeroes Theorem
-Find The Possible Number of Positive and Negative Zeros Of a Polynomial
-Find The Bounds On The Real Zeros of Polynomials
-Learn a Procedure For Finding The Real Zeros of a Polynomial Function
Term
The zeros of y=F(x) also equal the solutions of...
Definition
F(x)=0
Term
A real number r is rational if....
Definition
r=p/q for some integers p and q
{0, 1, 2, ....}
Term
If p/q is a rational zero p...
Definition
P/asubscrpt0 and q/asubscrptn
Term
How to Find All Possible Rational Zeroes
Definition
1.) Find the Factors of the Last Number In the Polynomial
2.) Find the Factors of the Leading Coefficient
3.) Pair off the factors of both and divide them to determine the rational zeros of the polynomial
Term
What are the rational zeros of:
5x^2+3x+2
Definition
1/5, 1, 2, 2/5
Term
What are the rational zeros of:
3x^3+2x^2+x-1
Definition
1, 1/3
Term
How do you find an additional zero, if a zero is given for a polynomial?
Definition
Find the conjugate
Term
If 1-sqrt2 is a zero of a polynomial, what is another zero of the polynomial?
Definition
1+sqrt2
Term
Why is 1+sqrt2, an additional zero in a polynomial with a zero of 1-sqrt2?
Definition
Because They Are Conjugates
Term
The number of variations of sign minus any even non-negative integer
[f(x)]
Definition
The number of positive zeros of P
Term
The number of negative zeros is
Definition
The number of variations of sign minus any even non-negative integer
[f(-x)]
Term
p(x)/x-k=
Definition
q(x)+[r(x)/x-k]
Term
If q(x) has positive coefficients and k>0, then k...
Definition
Is an upper bound on the roots of p
Term
If the signs of q(x) alternate and k>0, then k....
Definition
Is a lower bound on the roots of p
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