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 real and distinct roots?

A
$(-\infty, \infty)$
✓
$(-1,\infty)$
C
$\big[-1,\infty)$
D
$(-1,1)$

✓

Answer

Correct option: B.

$(-1,\infty)$

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

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