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Yogita Ingle 5 years, 7 months ago
Consider we have two numbers 78 and 980 and we need to find the HCF of both of these numbers. To do this, we choose the largest integer first, i.e. 980 and then according to Euclid Division Lemma, a = bq + r where 0 ≤ r ≤ b;
980 = 78 × 12 + 44
Now, here a = 980, b = 78, q = 12 and r = 44.
Now consider the divisor as 78 and the remainder 44 and apply the Euclid division method again, we get
78 = 44 × 1 + 34
Similarly, consider the divisor as 44 and the remainder 34 and apply the Euclid division method again, we get
44 = 34 × 1 + 10
Following the same procedure again,
34 = 10 × 3 + 4
10=4×2+2
4=2×2+0
As we see that the remainder has become zero, therefore, proceeding further is not possible and hence the HCF is the divisor b left in the last step which in this case is 2. We can say that the HCF of 980 and 78 is 2.
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Yogita Ingle 5 years, 7 months ago
Zeros of a polynomial can be defined as the points where the polynomial becomes zero on the whole. A polynomial having value zero (0) is called zero polynomial.
In general, If k is zero of the linear polynomial in one variable; P(x) = ax +b, then
P(k) = ak+b = 0
k = -b/a
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Posted by Sakshi Yadav 5 years, 7 months ago
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Yogita Ingle 5 years, 7 months ago
For the solution of this question we have to find L.C.M of 36 and 54.
L.C.M. of 36 and 54 = 2×2×3×3×3 = 108
Now,
The least number = (L.C.M. of 36 and 54) + 5
⇒ 108+5 = 113
Hence 113 is the least positive integer which on diminished by 5 is exactly divisible by 36 and 54.
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Yogita Ingle 5 years, 7 months ago
Let us assume √2 is rational number.
a rational number can be written into he form of p/q
√2=p/q
p=√2q
Squaring on both sides
p²=2q²__________(1)
.·.2 divides p² then 2 also divides p
.·.p is an even number
Let p=2a (definition of even number,'a' is positive integer)
Put p=2a in eq (1)
p²=2q²
(2a)²=2q²
4a²=2q²
q²=2a²
.·.2 divides q² then 2 also divides q
Both p and q have 2 as common factor.
But this contradicts the fact that p and q are co primes or integers.
Our supposition is false
.·.√2 is an irrational number.
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Aaryan Kumar 5 years, 7 months ago
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