To determine: Why every polynomial equation with real coefficients of degree 3 must have at least one real root. Solution: A polynomial equation with real coefficients of degree 3 must have at least on real root. Explanation: According to Fundamental Theorem of Algebra. n t h degree polynomial has exactly n t h roots. Also, if f ( x ) is a polynomial with real coefficients and x = a + i b solution of f ( x ) = 0 then x = a − i b is also a solution of f ( x ) = 0 . Hence, we can say that a cubic equation can have one real root and two complex roots or it can have three real roots Therefore, a cubic equation must have at least one real root.
To determine: Why every polynomial equation with real coefficients of degree 3 must have at least one real root. Solution: A polynomial equation with real coefficients of degree 3 must have at least on real root. Explanation: According to Fundamental Theorem of Algebra. n t h degree polynomial has exactly n t h roots. Also, if f ( x ) is a polynomial with real coefficients and x = a + i b solution of f ( x ) = 0 then x = a − i b is also a solution of f ( x ) = 0 . Hence, we can say that a cubic equation can have one real root and two complex roots or it can have three real roots Therefore, a cubic equation must have at least one real root.
Solution Summary: The author explains that a polynomial equation with real coefficients of degree 3 must have at least one real root.
To determine: Why every polynomial equation with real coefficients of degree 3 must have at least one real root.
Solution:A polynomial equation with real coefficients of degree 3 must have at least on real root.
Explanation:
According to Fundamental Theorem of Algebra.
n
t
h
degree polynomial has exactly
n
t
h
roots. Also, if
f
(
x
)
is a polynomial with real coefficients and
x
=
a
+
i
b
solution of
f
(
x
)
=
0
then
x
=
a
−
i
b
is also a solution of
f
(
x
)
=
0
. Hence, we can say that a cubic equation can have one real root and two complex roots or it can have three real roots Therefore, a cubic equation must have at least one real root.
Solve questions by Course Name (Ordinary Differential Equations II 2)
please Solve questions by Course Name( Ordinary Differential Equations II 2)
InThe Northern Lights are bright flashes of colored light between 50 and 200 miles above Earth.
Suppose a flash occurs 150 miles above Earth. What is the measure of arc BD, the portion of Earth
from which the flash is visible? (Earth’s radius is approximately 4000 miles.)
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