Question

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero.

f(x) = 1/4x^2(x^2-5)(x+3)

Answer 1

`f(x)=(1)/(4)x^2(x^2-5)(x+3)\\ x=0 \vee x=-\sqrt5 \vee x=\sqrt5 \vee x=-3`

x=0 is a double root and the graph touches the x-axis at it.
The rest zeroes are single ones and the graph crosses the x-axis at them.