A number of roots of a polynomial of fourth degree,

P4 ( x ) = a4 x4 + a3 x3 + a2 x2 + a1 x + a0,

depends on the coefficients of the polynomial. It can take on values  4, 3, 2, and zero (but not 1) as it is demonstrated by the figure.

Likewise, a number of roots of a polynomial of fifth degree,

P5 ( x ) = a5 x5 + a4 x4 + a3 x3 + a2 x2 + a1 x + a0,

takes on values  5, 4, 3, 2, and 1 (but not zero).
The simplest way of changing the number of roots is to change a value of the constant term  a0  or, equivalently, to change the position of the x-axis.

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