Question

if the zeroes of polynomial f(X)=x^3-3x+x+1 are a-b and a and a+b find a anb b

Answer 1

Sum of roots = -b/a

a-b + a + a+b = 0

a = 0

Now,

αβ + βγ + γα = -2

a² - b² = -2

b² = 2

$b \: = + \sqrt{2} \\ or \\ b \: = - \sqrt{2}$