The values of ‘a’ for which a2−1×2+2(a−1)x+2 is positive for any x,are

The values of ‘a’ for which a21x2+2(a1)x+2 is positive for any x,are

  1. A

    a1

  2. B

    a1

  3. C

    a>-3

  4. D

    a3 or a1

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    Solution:

    We know that the expression ax2+bx+c>0 for

    all x, if a>0 and b2<4ac

     a21x2+2(a1)x+20 for all x.

    a210 and  4(a1)28a210

    a210 and 4(a1)(a+3)0

     a210 and  (a1)(a+3)0

     a1 or,a1and a3 or,  a1

     a3 or, a1

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