Question

How many zeroes do the polynomials
$P_1\left(x\right)=x^3+x^2+x+1$ and
$P_2\left(x\right)=x^2+1$
have in common?

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

The correct option is A

1

$P_1\left(x\right)=x^3+x^2+x+1=(x+1)(x^2+1)$.
So, There are two factors of $P_1\left(x\right)$

$P_2\left(x\right)=x^2+1$
So, $x^2+1$ is common in both

Lets find zeroes of $x^2+1$, $x^2+1=0\Rightarrow x^2=-1$
$x=\sqrt{-1}=i$ Where $i$ is iota.
$\therefore$ Only one zero (i.e. $x$ = i) is common to both polynomials