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Paragraph: Let f( x )= x ^3-3 x +1, x R and a , b , c are roots of f( x )=0, P ( , f( )) is point of local minima Q ( , f( )) is point of local maxima and R ( , f( )) is point of inflection in the graph of y =f( x ) . On the basis of above information answer the following : Question: Triangle PQR is -

Options

  1. Aequilateral
  2. Bisosceles
  3. Cright angle
  4. Dnone of these

Correct answer

D. none of these

Step-by-step solution

aligned & f^ =3 (x^2-1 )=0 & x=1,-1 & =1, =-1 & f^ =0 aligned x =0 is point of inflection so P (1,-1) Q (-1,3) R (0,1) aligned & so P (1,-1) Q (-1,3) R (0,1) & = 1 2 | array ccc 1 & -1 & 1 -1 & 3 & 1 0 & 1 & 1 array |= 1 2 [2-1-1]=0 & so collinear aligned

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