[Math] The number of roots common between the two equations is

Question

The number of roots common between the two equations

$x^3+3x^2+4x+7=0$ and $x^3+2x^2+7x+5=0$ is

$\color{green}{a.)\ 0 } \\~\\
b.)\ 1 \\~\\
c.)\ 2 \\~\\
d.)\ 3 \\~\\ $

i tried to solve both equations by subtracting then

$x^3+3x^2+4x+7-(x^3+2x^2+7x+5)=0 \\
x^2-3x+2=0 \\
x=2, \ 1$

but the answer is given as option $a.)$

I look for a short and simple way.

I have studied maths up to $12$th grade. Thanks!

Answer 1

You've found the $x$ values where the two expressions are equal. However, at neither of these $x$-values are the expressions equal to $0$, which is what you need for roots.