Thursday, October 15, 2009

Crack competitions with Vedic math - IV | Transpose and Apply


Once again, in my last article I have described the third formula of Vedic mathematics.

Now today in this article I will explain the fourth formula of Vedic mathematics.

The Fourth formula is-

“Transpose and Apply”

The term Parāvartya Yojayet this means “Transpose and apply”.

In this term they provide an easiest way to solve the polynomial division.

So let’s start - here you can see 4 simple steps for polynomial division

We take an example for this formula -

Divide x3 + 7x2 + 6x + 5 by x – 2.

i.) x3 divided by x gives us x2 which is therefore the first term of the quotient

x3 7x2 6x 5

x 2

+ + +

Q = x2 + ….

ii.) x2 × –2 = –2x2 but we have 7x2 in the divident. This means that we have to get 9x2 more. This must result from the multiplication of x by 9x. Hence the 2nd term of the divisor must be 9x

x3 7x2 6x 5

x 2

+ + +

Q = x2 + 9x +….

iii.) As for the third term we already have –2 × 9x = –18x. But we have 6x in the dividend. We must therefore get an additional 24x. Thus can only come in by the multiplication of x by 24. This is the third term of the quotient.

Q = x2 + 9x + 24

iv.) Now the last term of the quotient multiplied by – 2 gives us – 48. But the absolute term in the dividend is 5. We have therefore to get an additional 53 from some where. But there is no further term left in the dividend.

This means that the 53 will remain as the remainder

Q = x2 + 9x + 24 and R = 53.21

Further I will explain the next formula of Vedic math.

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