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Question
Answer the following:
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b
Solution
f(x) = ax2 + bx + 2
f(1) = 3
∴ a(1)2 + b(1) + 2 = 3
∴ a + b = 1 ...(i)
f(4) = 42
∴ a(4)2 + b(4) + 2 = 42
∴ 16a + 4b = 40
Dividing by 4, we get
4a + b = 10 ...(ii)
Solving (i) and (ii), we get
a = 3, b = –2
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