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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 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.


What is a synonym for 'variety'?

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


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.


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.