Question

Number of transformed equations of x^3+2x^2+x+1=0 by eliminating third term is

Answer 1

)By Taylor’s theorem in powers of h

: Let f(x) be the given expression.  Suppose we want to know what f(x+h) is.

    By Taylor’s theorem, f(x+h) = f(x) + f’(x) h + (1/2!)(f’’(x).h2 ) +

(1/3!)(f’’’’(x).(h3) +……….(1/n!) (f’’’’’…. (n times) (hn))

       

        (ii) By Taylor’s thoerem in powers of x, by symmetry between x and h in the expansion:

Let f(x) be the given expression; suppose we want to know  what what f (x+h) is.

f(x+ h) = f(h) + x f’(h) + ((x2)/2!)f’’(h) + ((x3)/3!)f’’’(h) +…….((xn)/n!)(f’’’’’….

….(n times) (h).

Answer 2

Answer:

By Taylor’s theorem in powers of h:-

Let f(x) be the given expression, and we want to know what f(x+h) is.

By Taylor’s theorem,

f(x+h) = f(x) + f’(x) h + (1/2!)(f’’(x).h2 ) +(1/3!)(f’’’’(x).(h3) +……….(1/n!) (f’’’’’…. (n times) (hn))

By Taylor’s thoerem in powers of x, by symmetry between x and h in the expansion:

Let f(x) be the given expression; and we want to know what what f (x+h) is.

f(x+ h) = f(h) + x f’(h) + ((x2)/2!)f’’(h) + ((x3)/3!)f’’’(h) +…….((xn)/n!)(f’’’’’….….(n times) (h).

in last we have to use

Horner’s method:

To transform f(x) into f (x+h) ,we perform synthetic division by Horner’s method.

For this, we divide f(x) by x-h by Horner’s method. We write the coeffcients of the powers of x in descending order in a horizontal line and write the coefficient of the divisor on the vertical margin to the left, keeping the sign of the coefficeint of x the same but changing the sign of the other term, so as to convert subtraction more conveniently into one of addition.