Question

For the polynomial f(x)=x2−5x+4 with roots α and β. Find the value of α−β.

Answer 1

Let consider the roots as a,b

f(x)=x^2-5x+4=0

=x^2-4x-x+4=0

=x(x-4)-1(x-4)=0

= (x-4) (x-1)=0

x=4 or x= 1

a=4,b= 1

therefore,a-b=4-1=3