show thatp(x) = x3 -3x2 +2x -6 has only one zero.
If the question is, "show that p(x) = x3 – 3x2 + 2x – 6 has only one real zero".
Then the solution is as follows :
Given polynomial is:
Put x = 3, we get
⇒ x = 3 is a zero of p(x).
∴ (x – 3) must be a factor of p(x).
So, we can write,
To find another zeros, we must have
From (1), we don't get any real value of x.
Hence, the only real zero of p(x) is x = 3.