Question

I. $3p^2+17p+10=0$
II. $10q^2+9q+2=0$

• 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 B If p is smaller than q

Equation I
$3p^2+17p+10=0$
$\Rightarrow 3p^2+15p+2p+10=0$
$\Rightarrow 3p(p+5)+2(p+5)=0$
$\Rightarrow (p+5)(3p+2)=0$
$\Rightarrow p=-2$ or $-\frac{2}{3}$

Equation II
$10q^2+5q+4q+2=0$
$\Rightarrow 5q(2q+1)+2(2q+1)=0$
$\Rightarrow (2q+1)(5q+2)=0$
$\Rightarrow q=-\frac{1}{2}$ or $-\frac{2}{5}$
Hence, $p<q$