Consider the polynomials f ( t ) = t + 1 and g ( t ) = ( t + 2 ) ( t + k ) , where k is an arbitrary constant. For which values of the constant k are the three polynomials f ( t ) , t f ( t ) , and g ( t ) a basis of P 2 ?
Consider the polynomials f ( t ) = t + 1 and g ( t ) = ( t + 2 ) ( t + k ) , where k is an arbitrary constant. For which values of the constant k are the three polynomials f ( t ) , t f ( t ) , and g ( t ) a basis of P 2 ?
Solution Summary: The author explains how the three polynomials form a basis of P_2.
Consider the polynomials
f
(
t
)
=
t
+
1
and
g
(
t
)
=
(
t
+
2
)
(
t
+
k
)
, where k is an arbitrary constant. For which values of the constant k are the three polynomials
f
(
t
)
,
t
f
(
t
)
, and
g
(
t
)
a basis of
P
2
?
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY