<s>[INST] The number of roots common between the two equations is 
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!
 [/INST] Considering $$f(x)=x^3+3x^2+4x+7$$ $$g(x)=x^3+2x^2+7x+5$$ you could notice that their derivatives never cancel in the real domain. So, $f(x)=0$ has only one real root and same for $g(x)=0$. So, the maximum number of common roots is $1$.
Now, inspection : 


*

*$f(-3)=-5$, $f(-2)=3$; so the root for $f(x)=0$ is somewhere between $-3$ and $-2$.

*$g(-1)=-1$, $g(0)=5$; so the root for $g(x)=0$ is somewhere between $-1$ and $0$.


So, no common root.
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