Question

I. $p^2+5p+6=0$
II. $q^2+3q+2=0$

• A. If p is greater than q
• B. If p is smaller than q
• C. If p is equal to q
• D. If p is either equal to or greater than q
• E. If p is either equal to or smaller than q

Answer 1

The correct option is E If p is either equal to or smaller than q

Equation I
$p^2+5p+6=0$
$\Rightarrow p^2+3p+2p+6=0$
$\Rightarrow p(p+3)+2(p+3)=0$
$\Rightarrow (p+3)(p+2)=0$
$\Rightarrow p=-2$ or $-3$

Equation II
$q^2+3q+2=0$
$\Rightarrow q^2+q+2q+2=0$
$\Rightarrow q(q+1)+2(q+1)=0$
$\Rightarrow (q+1)(q+2)=0$
$\Rightarrow q=-1$ or $-2$
Hence, $p\le q$