Question

The set of values of '$p$' for which the expression $x^2-2px+3p+4$ is negative for at least one real $x$ is-

• A. $\varphi$
• B. $(-1,4)$
• C. $(-\infty ,-1)U(4,\infty )$
• D. $\{-1,4\}$

Answer 1

The correct option is C $(-\infty ,-1)U(4,\infty )$

It will be negative for atleast one real x if descriminant is greater than 0

$\Rightarrow 4p^2-12p-16>0$

$\Rightarrow p^2-3p-4>0$

$\Rightarrow (p-4)(p+1)>0$

$\Rightarrow p\in (-\infty ,-1)\cup (4,\infty )$