Question

For which values of $p$ is $p^2-5p+6$ negative?

• A. $p<0$
• B. $2<p<3$
• C. $x>3$
• D. $x<2$

Answer 1

The correct option is B $2<p<3$

Given $p^2-5p-5p+6$.The given expression factors into $(p-3)(p-2)$. If the expression is negative then the factors must have opposite signs. If $(p-2)$ is negative and $(p-3)$ is positive there are no such number. IT is only possible when $(p-3)$ is negative and $(p-2)$ is positive, then $p>2$ and $p<3$. So $2<p<3$ is the correct choice.