Question

If equation $P\left(x\right)=x^2+ax+1$ has two distinct real roots, then exhaustive values of $a$ are

• A. $(-2,2)$
• B. $(-\infty ,-2)\cup (2,\infty )$
• C. $(-2,\infty )$
• D. all real numbers

Answer 1

Answer: (B)

$(-\infty ,-2)\cup (2,\infty )$

Given equation is $P\left(x\right)=x^2+ax+1$

For the equation to have $2$ real distinct roots, its discriminant should be positive.
$\Rightarrow$ $D>0$
$\Rightarrow$ ${\left(a\right)}^2-4\left(1\right)\left(1\right)>0$
$\Rightarrow$ $a^2>4$
$\Rightarrow$ $a\in (-\infty ,-2)\cup (2,\infty )$
Hence, choice (B) is the correct answer.