Question

If f(x) = ax² + bx + 2 and f(1) = 3, f(4) = 42, find a and b.

Answer 1

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