Question

$p(x) = x^{3} - 3x^{2} + 2x - 6$ has only one zero prove.

Answer 1

Answer:

Step-by-step explanation:

$p(x)= x^3-3x^2+2x-6$

$p(x) = x^2 (x-3) +2 (x-3)\\\\p(x)= (x^2+2)(x-3)$

now if p(x) = 0. then, either $x^2+2$ = 0 or x-3 =0

but  $x^2+2$ can not be zero (because $x^2+2$ is always a positive number greater than 2.)

so, p(x) =0 only when x=3. so p(x) has only one zero x=3.