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Question

Let f(x)=(x21,  if 0<x<22x+3, if 2x<3, a quadratic equation whose roots are limx2f(x) and limx2+f(x) is 
  1. x26x+9=0
  2. x27x+8=0
  3. x214x+49=0
  4. x210x+21=0


Solution

The correct option is D x210x+21=0
Let us first find the roots of the required quadratic equation i.e.limx2f(x) = limx2x21= 41 = 3limx2+f(x) = limx2+2x+3= 2(2)+3 = 7Now, let us find the qudratic equation with roots as x=3 and x=7(x3)(x7)=0x210x+21=0

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