fx11x3x211x1 Find the real zeros Use the real zeros to facto

f(x)=11x^3-x^2+11x-1

Find the real zeros

Use the real zeros to factor f.

Solution

f(x) = 11x^3 - x^2 + 11x - 1

to find zeros of the function set f(x) = 0

11x^3 - x^2 + 11x - 1 = 0

rational zeros are

+- { 1 } / { 1 , 11 }

actual zero occur at x = 1/11

therefore, to find other zeros divide 11x^3 - x^2 + 11x - 1 by 11x - 1

on dividing we get x^2 + 1

setting x^2 + 1 = 0

x^2 = -1

x = + - i

therefore, 3 zeros are

x = 1/11

x = i

x = -i

factors are

11x^3 - x^2 + 11x - 1 = (11x -1 ) ( x^2 + 1)