MCQ
If the equation $ax^2+ 2x + a = 0$ has two distinct roots, if :
- ✓$\text{a}=\pm1$
- B$a = 0$
- C$a = 0, 1$
- D$a = -1, 0$
✓
Answer
Correct option: A.
$\text{a}=\pm1$
In the equation $ax^2+ 2x + a = 0$
$\Rightarrow D = b^2- 4ac$
$\Rightarrow D = (2)^2- 4 \times a \times a$
$\Rightarrow D = 4 - 4a^2$
Roots are real and equal
$\Rightarrow D = 0$
$\Rightarrow 4 - 4a^2= 0$
$\Rightarrow 4 = 4a^2$
$\Rightarrow 1 = a^2$
$\Rightarrow a^2= 1$
$\Rightarrow\text{a}^2=(\pm1)^2$
$\Rightarrow\text{a}=\pm1$
$\Rightarrow D = b^2- 4ac$
$\Rightarrow D = (2)^2- 4 \times a \times a$
$\Rightarrow D = 4 - 4a^2$
Roots are real and equal
$\Rightarrow D = 0$
$\Rightarrow 4 - 4a^2= 0$
$\Rightarrow 4 = 4a^2$
$\Rightarrow 1 = a^2$
$\Rightarrow a^2= 1$
$\Rightarrow\text{a}^2=(\pm1)^2$
$\Rightarrow\text{a}=\pm1$
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