Find the values of k1 and k2 such that (-1,0) and (1,0) are x-intercepts for the graph of f(x)=k1x^4 - k2x^3 + x - 4

Answer 1

To obtain k₁ and k₂, we can formulate two equations representing two lines in 2d space. The equations are:

k₁+ k₂ - 5 = 0

k₁ - k₂ - 3 = 0

Through elimination we obtain

2•k₁ - 8 = 0, k₁ = 4

With the found value of k₁, we then find the value of k₂ to be

4 - k₂ -3 = 0, k₂ = 1

Thus f(x) = 4x⁴ - x³ + x - 4