Pls solve here and pls dont send any link coz its confusing so pls give me answer - Maths - Polynomials

Question

Pls solve here and pls dont send any link coz its confusing so pls
give me answer to my question here only!

Ajanta Trivedi · Accepted Answer

the given polynomial is: $f (x) = x^{3} - 3 x^{2} + x + 1$

the zeroes of f(x) are (a-b), a and (a+b).

sum of the zeroes = - coefficient of $x^{2}$ / coefficient of $x^{3}$

$a - b + a + a + b = - \frac{- 3}{1} 3 a = 3 \Rightarrow a = 1$ ..............(1)

product of zeroes = - constant term / coefficient of $x^{3}$

$(a - b) a (a + b) = - \frac{1}{1} a (a^{2} - b^{2}) = - 1.......... (2)$

put a =1 in eq(1):

$1 (1^{2} - b^{2}) = - 1 1 - b^{2} = - 1 b^{2} = 1 + 1 = 2 b = \pm \sqrt{2}$

thus $a = 1 a n d b = \pm \sqrt{2}$

hope this helps you.

cheers!!

Pls solve here ...and pls dont send any link coz its confusing so pls give me answer to my question here only!