Home
Class 12
MATHS
If both roots of the equation x^(2)-2 a ...

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

A

`R`

B

`(-1,1)`

C

`(-2,2)`

D

`(-3,-1)uu(1,3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `f(x)=x^(2)-2ax+a^(2)-1`
Now four cases arise:
Case I `Dge0`

`implies(-2a)^(2)-4.1(a^(2)-1)ge0`
`implies 4ge0` ltbr.gt `:.a epsilonR`
Case II `f(-2)gt0`
`implies4+4a+a^(2)-1gt0`
`impliesa^(2)+4a+3gt0`
`implies(a+1)(a+3)gt0`
`:.a epsilon(-oo,-3)uu(-1,oo)`
Case III `f(2)gt0`
`implies4-4a+a^(2)-1gt0`
`impliesa^(2)-4a+3gt0`
`implies(a-1)(a-3)gt0`
`:.a epsilon(-oo,1)uu(3,oo)`
Case IV `-2ltx` coordinate of vertex `lt2`
`implies-2lt2alt2`
`:.a epsilon(-1,1)`
Hence `[a]=-1,0`
Promotional Banner

Similar Questions

Explore conceptually related problems

Roots of the equation x^(2) -2x+ 1 =0 are :

Roots of equation x^(2)-2x+1=0 are:

Find the roots of the equation 2x^(2) + 10 x + 20 =0

The roots of the equation 12 x^2 + x - 1 = 0 is :

The roots of the equation |x^(2)-x-6|=x+2 are

All the values of m for which both roots of the equation x^(2)-2 m x+(m^(2)-1)=0 are greater than -2 but less than 4 lie in the interval

The roots of the equation x^(2)-2sqrt(3)x+3=0 are

If the roots of the equation x^(2)-lx+m=0 differ by 1, then

The roots of the quadratic equations x^(2) - 5x -6=0 are

If both the roots of the quadratic equation x^(2)-2 k x+(k^(2)+k-5)=0 are less than 5, then k lies in the interval