For polynomial f(x)=x^5-2x^4+8x^2-13x+6 , reply the following questions.
(a) How many zeros does function have over set of complex numbers?
(b)Find maximum number of local extrema (maxima or minima) graph of function can have?
(c) Complete given statements:
As x ---> ? , f(x) --->________
As x ----> - ? , f(x) ---> ________
(d) Write the possible rational zeros of the function.
(e) Factor the polynomial completely over set of complex numbers.
2) For questions graph conic section. Ensure to comprise any foci, asymptotes, and vertices.
i. Graph (x-2)^2/36+(y+1)^2/25=1
ii. Graph (y+3)^2/9-(x-2)^2/16=1
3. Richter scale is utilized to measure magnitude of the earthquake. Magnitude, R, is given by equation: R=0.65 log (0.39E)+1.45, where E is energy (measured in kilowatt-hours) released by earthquake. Find out amount of energy released by the earthquake of magnitude 7.5.
4. Graph function, then define domain and range. y=x/x^2-4
5. Utilize synthetic division to determine quotient and the remainder.
(12x^4+5x^3+3x^2-5)+(x+1)