Question

Find all values of parameter $a$ for which the quadratic equation $(a+1)x^2+2(a+1)x+a-2=0$ has two distinct roots.

• A. $a\in (-1,\infty )$
• B. $a\in (-\infty ,-1)$
• C. $a\in (-1,1)$
• D. $a\in (-\infty ,\infty )$

Answer 1

The correct option is A $a\in (-1,\infty )$

Discriminant of the given quadratic equation is,
$D=4{(a+1)}^2-4(a+1)(a-2)=4(a+1)(a+1-a+2)=12(a+1)$
Now for two distinct roots,
$D>0\Rightarrow a+1>0$
$\Rightarrow a\in (-1,\infty )$.