Question

determine the value of k if g(x)=4x+k is a tangent to f(x)=-x²+8x+20​

Answer 1

Step-by-step explanation:

if it is a tangent to the function then it must satisfy the equation and be a solution to it. therefore, g(x) is a factor of f(x).

let, f(x) = 0

x^2 +8x +16 +20 - 16 = 0

(x+4+2)(x+4-2)=0

therefore,

either, or,

4x+k = x+6 4x+k=x+2

implies that, implies that,

k= 3(2-x) k = 2-3x

therefore, k = {3(2-x),2-3x}