Complete
the
factor
tree
for
the
given
polynomials
f
(
x
)
and
g
(
x
)
.
Hence
find
Thinking Corner
GCD and LCM.
f(0) = 223 - 922 - 326 -21
g(0) = 2x - 722 - 43.1 - 42
2x + 3
x + 2
x + 1
GCD [f(x) and g(x)] =
LCM f(a) and g()]
Answers
Step-by-step explanation:
11th
Maths
Binomial Theorem
Special Cases of Binomial Theorem
If n is a positive integer ...
MATHS
If n is a positive integer and (3
3
+5)
2n+1
=α+β where α is an integer and 0<β<1, then
THIS QUESTION HAS MULTIPLE CORRECT OPTIONS
HARD
Share
Study later
ANSWER
Consider (3
3
+5)
2n+1
−(3
3
−5)
2n+1
=α
Solving the above expression, only even terms were left in the binomial expansion,
2×(
2n+1
C
1
3
3
2n
5+
2n+1
C
3
3
3
2n−2
5
3
+⋯+
2n+1
C
2n+1
5
2n+1
)=α
Take 2 and 5 common out of this expression, then it becomes:
10×(…)=α
(3
3
+5)
2n+1
=α+(3
3
−5)
2n+1
β=(3
3
−5)
2n+1
β is always less than 1.
Option A:
α is an even integer, i.e. α=2×5×(…)
Option B:
(α+β)
2
is not divisible by 2
2n+1
,β contains a irrational number.
Option C:
Integer Just below (3
3
+5)
2n+1
is not divisible by 3.
Check for n=1, it does not satisfy.
Option D: