Question

If f(x) = ax² − bx + 6 and f(2) = 3 and f(4) = 30, find a and b

Answer 1

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