If, (a+1)x^2+2(a+1)x+(a-2)=0 then, for what parameter of 'a ' the… - Vidyadip

MCQ

If, $(\text{a}+1)\text{x}^2+2(\text{a}+1)\text{x}+(\text{a}-2)=0$ then, for what parameter of $'a\ '$ the given equation have imaginary roots?

✓
$(-\infty,-1)$
B
$(-1,\infty)$
C
$(-1, 1)$
D
$(-\infty,\infty)$

✓

Answer

Correct option: A.

$(-\infty,-1)$

For, imaginary roots, $\text{D}>0$
Where, $\text{D}=\text{b}^2-4\text{ac}$
In the equation, $(\text{a}+1)\text{x}^2+2(\text{a}+1)\text{x}+(\text{a}-2)=0$
$\text{D} = \Big[2(\text{a}+1)\Big]^2 – 4 (\text{a} + 1)(\text{a} – 2)$
$= 4\text{a}^2 + 4 + 8\text{a} – 4({\text{a}^2 – 2\text{a} + \text{a} – 2})$
$= 4\text{a}^2 + 4 + 8\text{a} – 4{\text{a}^2 – 4\text{a} +8<0}$
$\Rightarrow12\text{a}+12<0$
$\Rightarrow12\text{a}<-12$
$\Rightarrow\text{a}<-1$
$\therefore\text{a}\in(-\infty,-1)$

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