Question

Given the zeros of the function f (x) = x4 + 3x3 – 28x², identify whether the zero is a bounce or

Answer 1

Assuming the function is

f(x) = x^4 + 3x^3-28x^2

Factorising, we get

f(x) = x^2(x+7)(x-4)

Therefore, there is a double root at x = 0 and singular roots at x = -7 and 4

double roots tend to bounce, kind of like the standard quadratic y = x^2

singular roots tend to cross, kind of like a straight line on a graph, y = mx + b

Therefore, it bounces at x = 0, and crosses at x = -7 and 4

In general, a root raised to an even power bounces, and a root raised to an odd power crosses.