Question

The roots of the equation $(p-2)x^2+2(p-2)x+2=0$
are not real when

• A. $p\in [1,2]$
• B. $p\in [2,3]$
• C. $p\in (2,4)$
• D. $p\in [3,4]$

Answer 1

The correct option is C $p\in (2,4)$

Roots of $(p-2)x^2+2(p-2)x+2=0$ are not real.
$\Rightarrow \Delta <0$
$\Rightarrow 4(p-2{)}^2-8(p-2)<0$
$\Rightarrow (p-2{)}^2-2(p-2)<0$
$\Rightarrow (p-2)(p-4)<0$
$\therefore p\in (2,4)$
Hence, option C.