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Sia ? 4 years, 3 months ago
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
Posted by Karan Johar 4 years, 4 months ago
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Posted by Deepak Paul 4 years, 4 months ago
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Preeti Dabral 4 years, 4 months ago
suppose √8 = a/b with integers a, b
and gcd(a,b) = 1 (meaning the ratio is simplified)
then 8 = a²/b²
and 8b² = a²
this implies 8 divides a² which also means 8 divides a.
so there exists a p within the integers such that:
a = 8p
and thus,
√8 = 8p/b
which implies
8 = 64p²/b²
which is:
1/8 = p²/b²
or:
b²/p² = 8
which implies
b² = 8p²
which implies 8 divides b² which means 8 divides b.
8 divides a, and 8 divides b, which is a contradiction because gcd (a, b) = 1
therefore, the square root of 8 is irrational.
Posted by Sahil Alam 4 years, 4 months ago
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Preeti Dabral 4 years, 4 months ago
second number = 153
Explanation:
Let first number = a,
second number = b
a = 27 ( given )
HCF(a,b) = 9
and
LCM (a,b) = 459
To find:
Value of b
solution:
We know that,
$\implies b = \frac{9\times 459}{27}$
After cancellation, we get
$\implies b = 153$
Therefore,
second number = b = 153
Posted by Bhumika Sharma 4 years, 4 months ago
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Sia ? 4 years, 4 months ago
let a be any positive integer
a=6q+r where 0< or equal to r <6
put r=1: a=6q+1 =odd integer
r=3: a=6q+3=odd integer
r=5: a=6q+5=odd integer
therefore,any positive odd integer is of the form 6q+1,6q+3 or 6q+5,where q is some integer
Posted by Rakesh Panda 4 years, 4 months ago
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Sia ? 4 years, 4 months ago
a sequence of numbers in which each differs from the preceding one by a constant quantity (e.g. 1, 2, 3, 4, etc.; 9, 7, 5, 3, etc.).
Aditya Sharma 4 years, 4 months ago
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Leitanthem Denel [Youtube] 4 years, 4 months ago
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Sia ? 4 years, 4 months ago
Let assume that 7-2root3 be rational and rational numbers are in the form of p/q form.
We know that root 3 is irrational and not p/q form. It contradicts the statement that it is irrational as it is p/q form.
Subtraction and multiplication of irrational number form irrational number so 7-2root3 is irrational.
Posted by Butterfly Teachings 4 years, 4 months ago
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Posted by Gouri Yaswanth Kumar 4 years, 4 months ago
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Sia ? 4 years, 4 months ago
Lets take assumed mean, A as 16
Class interval =2
∴ui=hxi−A=2xi−16
Now, we have A=16,xˉ=18 and h=2
We know that,
Mean, xˉ=A+h(N1∑fiui)
⇒18=16+2(f+442f+24)
⇒f+442f+24=1
⇒f+44=2f+24
⇒f=20
Hence, the value of missing frequency, f=20
Posted by Gajanan Torgal 4 years, 4 months ago
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Gouri Yaswanth Kumar 4 years, 4 months ago
Posted by Imran Khan 4 years, 4 months ago
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Preeti Dabral 4 years, 4 months ago
2x+3y=-5 (1)
3x-2y=12 (2)
Add eq 1 and 2 we get
5x+1y=7 (3)
Now
Subtract 1 from 2,we get
X-5y =17 (4)
Multiply 3 by 5 we get,
25x+5y=35 (5)
Now ,
Add 4 and 5 we get,
26x=52
X=2
now ,
Substitute x=2 in eq3
5x+1y=7
5×2+1y=7
10+y=7
y=7-10
y=-3
(x,y)=(2,-3)
Posted by Bhavesh B Nair 4 years, 4 months ago
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Preeti Dabral 4 years, 4 months ago
p(x)=3x²-2k+1
zeroes=α,7α
sum of zeroes= - b/a
α+7α= -(2k/3)
8α=2k/3
8α×3=2k
24∝=2k
k=12∝ (1)
product of zeroes= c/a
∝×7∝=1/3
7∝²=1/3
∝²=1/(3×7)
∝²=1/21
∝=±1/√21
∵∝=±1/√21
∴k=12(±1/√21)
k = ±12/√21
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Ketan Bapna 4 years, 4 months ago
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