Question

Let $a{x}^2+a^{2}x+2=0$ be a quadratic equation, $a\in R$ and $S$ be the set of values of $a$ for which roots of this equation are imaginary or equal, then answer the following questions:

Number of integral values of $a$ in set $S$ are

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Consider,
$a{x}^2+a^{2}x+2=0$ has imaginary or equal roots if
$(a^2{)}^2-4(2\left)\right(a)\le 0$
$a(a^3-8)\le 0$
$a(a-2)(a^2+4+2a)\le 0$
$aϵ(0,2](a\ne 0)$
$\therefore S\equiv (0,2]$$\to 0$ can't be included as above equation can.t be quadratic.
number of integral values in set S is 2