Log in
Sign up for FREE
arrow_back
Library
3.6
By Kevin Struble
star
star
star
star
star
Share
share
Last updated over 4 years ago
5 questions
Add this activity
1
1
1
1
1
Question 1
1.
The
Rational Root Theorem
states:
If a polynomial
P
(
x
) has integer coefficients, then every rational root of P(x)=0 can be written in the form p/q, where
where
p
is a factor of the constant term and
q
is a factor of the leading coefficient of P(x).
where
p
is the leading coefficient and
q
is the constant term of P(x).
Question 2
2.
The
Irrational Root Theorem
states:
If a polynomial P(x) has rational coefficients, and a+b\sqrt{c} is a root of P(x)=0, where a
and b
are rational and \sqrt{c} is irrational, then
a+b\sqrt{c} is also a root of P(x).
b-a\sqrt{c} is also a root of P(x).
a-b\sqrt{c} is also a root of P(x).
Question 3
3.
The
Complex Root Theorem
states:
If a polynomial P(x) has real coefficients, and a+bi is a root of P(x)=0, where a
and b
are real numbers, then its complex conjugate
b-ai is also a root of P(x).
a+bi is also a root of P(x).
a-bi is also a root of P(x).
b+ai is also a root of P(x).
Question 4
4.
The
Fundamental Theorem of Algebra
states that every polynomial function of degree n≥1
has at least two zeros in the set of complex numbers.
no zeros in the set of complex numbers.
has at least one zero in the set of complex numbers.
has at least one zero in the set of real numbers.
Question 5
5.
The
Corollary to the Fundamental Theorem of Algebra
states that iIncluding multiplicities, a polynomial function of degree n≥1
has exactly n+1
zeros.
has exactly n
zeros.
has exactly n-1
zeros.
where
p
is the constant term and
q
is the leading coefficient of P(x).
where
p
is a factor of the leading coefficient and
q
is a factor of the constant term of P(x).
b+a\sqrt{c} is also a root of P(x).
has at least n
zeros.