Question

(a) Find the Fourier series half-range Cosine series for the function f(x)=1-x, 0<x<π​

Answer 1

Answer:

given,

Zeroes are 1/2+2√3 and 1/2-2√3

sum of zeroes = 1/2+2√3 + 1/2-2√3

= 1/2 + 1/2

= 1

product of zeroes = 1/2+2√3 x 1/2-2√3

= [ 1/2 ] ² - [ 2√3 ]²

= 1/4 - 12

= 1/4 - 48 / 4

= -47 /4

Quadratic equation

x² - [ sum of zeroes ]x + product of zeroes

=x² - x + -47/4............