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Yogita Ingle 4 years, 5 months ago
(a -b) (a+ b) = a2 - b2
(4+√5) (4-√5) = (4)2 - (√5)2 = 16 - 5 = 11
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Krishna Chauhan 4 years, 5 months ago
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Gaurav Seth 4 years, 5 months ago
the rational number between √2 and √3
√2 = 1.414.
√3= 1.732.
So, a rational number between those two would be 1.5 (3/2). But there are several more, in fact, infinite number of rational numbers between √2 and √3.
Posted by Awadhesh Mishra 4 years, 5 months ago
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Posted by Awadhesh Mishra 4 years, 5 months ago
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Gaurav Seth 4 years, 5 months ago
For representing on a number line, we can opt for the following steps –
a.) Draw a number line of two points (units) from an initial point say. 0 in the right/positive direction
b.) Let those two points represent A & B respectively.
c.) Now, draw a line of 1-unit perpendicular to B and let it be called as C
d.) Join OC to represent the hypotenuse of a triangle, right angled at B
e.) This hypotenuse of triangle ABC is showing a length of
f.) We can use a divider and with the length of the hypotenuse, we can make a cut upon the number line.
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Unnati Kumawat 4 years, 5 months ago
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Rahul Rohit 4 years, 5 months ago
Yogita Ingle 4 years, 5 months ago
It is little tedious to divide 2 polynomials using the process described in previous section, So we use Remainder theorem.
Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).
Proof: Let p(x) be any polynomial with degree greater than or equal to 1. Suppose that when p(x) is divided by x – a, the quotient is q(x) and the remainder is r(x), i.e., p(x) = (x – a) q(x) + r(x) -- (i)
Since the degree of x – a is 1 and the degree of r(x) is less than the degree of x – a, the degree of r(x) = 0. This means that r(x) is a constant, say r. Thus we can re-write eq (i) as p(x) = (x – a) q(x) + r –(ii)
In particular, if x = a, then eq (ii) becomes p(a) = (a – a) q(a) + r = r,
Question: Find the remainder when p(x) = x4 + x3 – 2x2 + x + 1 is divided by x – 1.
Solution: Zero of x – 1 is 1, so as per remainder theorem remainder in this case will be p(1) .
So, p(1) = (1)4 + (1)3 – 2(1)2 + 1 + 1 = 2
Posted by Arjun Vishwakarma 4 years, 5 months ago
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Unnati Kumawat 4 years, 5 months ago
Yogita Ingle 4 years, 5 months ago
Frequency : The number of oscillations per unit time is called the Frequency of the sound wave. The number of compressions or rarefactions that cross a given point in per unit time is the frequency of the wave. It is denoted by μ and is unit is Hz (Hertz).
Sanjaya Kumar Behera 4 years, 5 months ago
Posted by Khushi Shah 4 years, 5 months ago
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