Question

a polynomial equation
${x}^{3 } + 2x + 3$
has
options

a. three imaginary zeros
b. one +ve and two imaginary zeros
c. one -ve and two imaginary zeros
d. three real zeroes​

Answer 1

Answer:

The correct answer is option (c)

Step-by-step explanation:

Given polynomial is

        $P(x)=x^3+2x+3$

Observe $P(-1)=(-1)^3+2(-1)+3=0$

So using factor theorem $x+1$ is factor of P(x)

Thus P(x) can be written as

                   $P(x)=(x+1)(x^2-x+3)$,

   ( second factor can be obtained by dividing P(x) by x+1 )

Now discriminant of $x^2-x+3$ is $=b^2-4ac=1-4(3)=-11<0$

Thus zeroes of the second factors are imaginary

Hence given polynomial has one negative (-1) and two imaginary roots