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
$\Rightarrow D = 0$
$\Rightarrow 4 - 4a^2= 0$
$\Rightarrow 4 = 4a^2$
$\Rightarrow 1 = a^2$
$\Rightarrow a^2= 1$
$\Rightarrow\text{a}^2=(\pm1)^2$
$\Rightarrow\text{a}=\pm1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The number of zeroes for a polynomial $p(x)$ where graph of $y = p(x)$ is given in Figure, is :
→The sum of first $40$ positive integers divisible by $6$ is :
→$x=2, y=1$ is a solution of the linear equation
→In the given circle, $O$ is a centre and $\angle B D C=42^{\circ}$, then $\angle A C B$ is equal to
→In the given figure, $AD =2 \ cm, DB =3 \ cm, DE =2.5 \ cm$ and $\ce{DE \| BC}$. The value of $x$ is:
→If the points $A(1, 2), O(0, 0)$ and $C(a, b)$ are collinear, then :
→Choose the correct option and justify your choice : $\frac{2\tan30^\circ}{1-\tan^230^\circ}= $
→Which of the following equations has $2$ as a root ?
→The zeros of the polynomial $x^2-2 x-3$ are :
→$\pi$ is :
→