If the equation ax2 + 2x + a = 0 has two distinct roots, if
Question:

If the equation $a x^{2}+2 x+a=0$ has two distinct roots, if

(a) $a=\pm 1$

(b) $a=0$

(c) $a=0,1$

(d) $a=-1,0$

Solution:

The given quadric equation is $a x^{2}+2 x+a=0$, and roots are distinct.

Then find the value of a.

Here, $a=a, b=2$ and, $c=a$

As we know that $D=b^{2}-4 a c$

Putting the value of $a=a, b=2$ and, $c=a$

$=(2)^{2}-4 \times a \times a$

$=4-4 a^{2}$

The given equation will have real and distinct roots, if $D>0$

$4-4 a^{2}=0$

$4 a^{2}=4$

$a^{2}=\frac{4}{4}$

$a=\sqrt{1}$

$=\pm 1$

Therefore, the value of $a=\pm 1$

Thus, the correct answer is $(a)$

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