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Complex Numbers and Quadratic Equations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
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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