Question

Find a polynomial f(x) of degree 4 that has the following zeros. 2, 5, 0, -7

Answer 1

Explanation:

f(x) = (x - 2)(x - 5)x(x+ 7)

f(x) = (x^2 - 7x + 10)*x * (x + 7)

f(x) = x(x^3 - 39x + 70)

f(x) = x^4 - 39x^2 + 70x

To show that this is correct, I've made a graph with these points labeled. The graph is just around the x axis. The local maximums and minimums are just too large a value.