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Question
If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b
Solution
f(x) = ax2 − bx + 6
f(2) = 3
∴ a(2)2 − b(2) + 6 = 3
∴ 4a – 2b + 6 = 3
∴ 4a – 2b + 3 = 0 ...(i)
f(4) = 30
∴ a(4)2 − b(4) + 6 = 30
∴ 16a – 4b + 6 = 30
∴ 16a – 4b – 24 = 0 ...(ii)
By (ii) – 2 × (i), we get
8a – 30 = 0
∴ a = `30/8 = 15/4`
Substituting a = `15/4` in (i), we get
`4(15/4) - 2"b" + 3` = 0
∴ 2b = 18
∴ b = 9
∴ a = `15/4`, b = 9
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