The function hx 2x3 3x2 x 1 has 2 real roots and 1 imagina

The function h(x) = 2x3 3x2 + x 1 has 2 real roots and 1 imaginary root.

Is this true or false and why?

A step-by-step would really help, thanks

Solution

false

all the coefficients of the polynomial are real numbers

so the function cannot have single imaginary root

if the function as a imaginary root then its conjugate also has to be the root of polynomial

but here its given only one imaginary root

so statement is false

h(x) = 2x3 3x2 + x 1 has 1 real roots and 2 imaginary roots .