Question

The function f(x)=bx^2+x-7 has a remainder of 3 when divided by (x-2), where b is a real constant.Find the value of b

Answer 1

Step-by-step explanation:

f(x) = bx² + x - 7

g(x) = x — 2

Remainder is 3.

Let us find the zero of g(x).

→ g(x) = 0

→ g(x) = x - 2

→ 0 = x - 2

→ x = 2

Now, as when f(x) is divided by g(x), then remainder is 3. So,

→ f(2) = 2

→ b(2)² + 2 - 7 = 2

→ 4b - 5 = 2

→ 4b = 7

→ b = 7/4

Therefore, the answer is 7/4.