Question

If both roots of the equation x^2 - 2ax + a^2 - 1 = 0 lie between (-2,2) then [a] can be​

Answer 1

Step-by-step explanation:

The given equation x

2

−2ax+a

2

−1=0

⇒(x−a)

2

−1

2

=0

⇒(x−a+1)(x−a−1)=0

⇒x=a−1,x=a+1

Thus, the roots are a−1 and a+1.

Also, a+1>a−1.

For these roots to lie between −2 and 2, we must have

a−1>−2 & a+1<2

⇒a>−1 & a<1

⇒−1<a<1

⇒[a]=−1,0.