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Question :
Let f(x) = x2 + ax + b and g(x) = f(x + 1) - f(x - 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is
Started 3 months ago by Shashank in
Option C
is the correct answer.
Explanatory Answer
g( 20) = f(21) – f(19)
72 = 21 2 + 21a + b – (19 2 + 19a + b)
72 = 40*2 + 2a
2a = -8
a = -4
f(x) = x 2 - 4x + b
Now, f(x) ≥ 0 for all real x
Therefore, D ≤ 0
16 – 4b ≤ 0
16 ≤ 4b
4 ≤ b
Hence, smallest possible value of b is 4
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