Question

If two zeros of a polynomial x cube minus 4 x square + 2 x are 2 minus root 2 and 2 + root 2.
Then find the third zero

Answer 1

let's see
we have the polynomial
x³-4x²+2x
let zeros are p = 2-√2, q = 2+√2 and r= ?

according to formula,

always remember that every cubic polynomial has this structure

[x³ - ( p+q +r)x²+ ( pq + qr + pr ) x - pqr ]

so,

p+ q + r = 4
put the values of p and q,

2-√2 + 2+ √2 + r = 4
=> r = 4 - 4
=> r = 0
thus third zero of polynomial is 0. answer

if you want to check it, see
pqr = 0

put the value of p,q and r

(2-√2).(2+√2).0 = 0

I hope that it will help you provided always remember the above formula.