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What is the multiplicity of the zero of the polynomial function f x x plus 5 4?

If you meant x + 5 = 4 then the multiplicity is 1.


What is a synonym for 'variety'?

collection, diversity, assortment, selection, multiplicity, array, range, mixture, change, variability, variation


What is the discriminant of an equation that is zero?

The discriminant of the zero polynomial, P(x) = 0, is zero because it has multiple roots at every point: For all x, P'(x) = P(x) = 0. Thus, the formula for the discriminant gives Δ = a_0^(0-2) * Π_{all different roots counting multiplicity} (one root - other root)^2 Note that the second term contains an uncountable number of zeroes multiplied together. Dividing out two of them leaves you with an uncountable number of zeroes multiplied together-- i.e. zero. The above argument can be made more rigorous by adding in all the limits and stuff.


Can a fourth degree polynomial touch the x axis three times?

No, a fourth degree polynomial cannot touch the x-axis three times. A polynomial can touch the x-axis at an even number of points, which corresponds to the multiplicity of its roots. If it touches the x-axis at three points, one of those points would have to be of odd multiplicity, which would make the total multiplicity odd, contradicting the fact that a fourth degree polynomial has an even degree. Thus, it can touch the x-axis at either 0, 2, or 4 points.


When graphing polynomials the x intercept of tye curve are xalled?

When graphing polynomials, the x-intercepts of the curve are called the "roots" or "zeros" of the polynomial. These are the values of x for which the polynomial equals zero. Each root corresponds to a point where the graph crosses or touches the x-axis. The multiplicity of each root can affect the behavior of the graph at those intercepts.