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KVPY2011MathematicsQuadratic Equation

Let f(x)=a x²+b x+c , where a, b, c are integers. Suppose f(1)=0,40 < f(6) < 50,60 < f(7) < 70 , and 1000 t < f (50) < 1000( t +1) for some integer t . Then the value of t is

Options

  1. A2 .
  2. B3
  3. C4
  4. D5 or more

Correct answer

C. 4

Step-by-step solution

array l f ( x )= ax ²+ bx + c given f (1)=0 a + b + c =0 and 40 < f (6) < 50 40 < 36 a +6 ~b + c < 50 40 < 35 a +5 ~b < 50 8 < 7 a + b < 10 7 a + b = integer =9 and 60 < f (7) < 70 60 < 49 a +7 ~b + c < 70 60 < 48 a +6 ~b < 70 10 < 8 a + b < 11.6 8 a + b = integer =11 array Solving (1) &(2) array l a=2, b=-5, c=3 f(x)=2 x²-5 x+3 f(50)=4753 1000 t < f(50) < 1000(t+1) (1000 4) < 4753 < 1000(4+1) t=4 array

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