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

fx-k1x4-k2x3x-4

#1

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

Answer:

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) = 4x^4 - x^3 + x - 4