Question

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

Answer 1

CORRECT QUESTION:

If the equation ax²+2x+a=0 has distinct roots,find the value of a.

Solution

Given Equation,

ax²+2x+a=0

On comparing with Ax²+Bx+C=0,

A=a,B=2 and C=a

Given that the above equation has distinct roots

Implies,

D>0

→B² - 4AC>0

→2² -4a² > 0

→4 - 4a² > 0

→1 - a² > 0

→ 1 > a²

→a < 1

For a < 1,the above equation has distinct and real roots

Answer 2

Answer:

The value of  a = < 1.

Step-by-step explanation:

The Accurate Question :

If the quadratic equation ax² + 2x + a = 0 has two distinct roots if a = ?

To Find :

The value of 'a'.

Solution :

Given :

Quadratic equation - ax² + 2x + a = 0.

Discriminant - b - 4ac

Now,

⇒ (2)² - 4 × a × a

⇒ 4 - 4a².

We know...

For distinct roots :

$\bigstar$ Discriminant >0

Now..

$\sf \\\implies B^2- 4AC>0\\ \\\implies 2^2 -4a^2 > 0\\ \\ \implies 4 - 4a^2 > 0\\ \\ \implies 1 - a^2 > 0\\ \\ \implies 1 > a^2\\ \\\implies <1$

∴ For a < 1,the above equation has distinct and real roots.