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