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Manipal MET2010MathematicsTrigonometric Equations

The number of values of the triplet (a, b, c) for which a 2 x+b ^2 x+c=0 is satisfied by all real x , is

Options

  1. A0
  2. B2
  3. C3
  4. Dinfinite

Correct answer

D. infinite

Step-by-step solution

a 2 x+b ^2 x+c=0 a (1-2 ^2 x )+b ^2 x+c=0 ie, (b-2 a) ^2 x+(a+c)=0 It is an identity, if b-2 a=0, a+c=0 , so a 1 = b 2 = c -1 Thus, number of triplet (a, b, c) are infinite.

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