Question

If the equation ax² + 2x + a = 0 has two distinct roots, if
A. a = ±1
B. a = 0
C. a = 0, 1
D. a = – 1, 0

Answer 1

The distinct roots for the given quadratic equation is a=-1,0

Step-by-step explanation:

Given quadratic equation is $ax^2+2x+a=0$

To find which is the distinct roots for the given quadratic equation :

• Comparing the given equation with general quadratic form $Ax^2+Bx+C=0$,
• we have A=a, B=2 and C=a
• Also given that the given quadratic equation has distinct roots
• Therefore we have that, D>0
• Hence $B^2-4AC>0$ ( if roots are distinct )

Substitute the values we get

• $2^2-4(a)(a)>0$
• $4-4a^2>0$
• $4(1-a^2)>0$
• $1-a^2>\frac{0}{4}$
• $1-a^2>0$
• $1>0+a^2$
• $1>a^2$
• Rewritting we get
• $a^2<1$
• $a<1$

For a < 1 the given quadratic equation has distinct and real roots

That is "a" must be -1 and 0

Therefore the option D) a=-1,0 is correct