Question

If a zero is , then the graph of its function only touches the x–axis at that zero.

Answer 1

if a solution or zero, has a multiplicity more than 1, namely appears there twice or more, like say (x - 3)³ = 0, that's (x-3)(x-3)(x-3) = 0, and gives the zeros of x = 3, x = 3 and x =3, it has a multiplicity of 3 in this case.

now, if a zero has an EVEN multiplicity, like 2 or 4 or 8 or 12, the graph only hits the x-axis there, and bounces right back, it doesn't cross it, at that point.

if it has an ODD multiplicity, it does cross the x-axis at that point.

Answer 2

The first one is: If a zero is of even multiplicity, then the graph of its function only touches the x–axis at that zero.

The second one is: If a zero is of odd multiplicity, then the graph of its function crosses the x–axis at that zero.