For the polynomial p(x) = 10x^4 + 21x^3 + 25x^2 + 16x - 12 (a) list all the poss
ID: 3014220 • Letter: F
Question
For the polynomial p(x) = 10x^4 + 21x^3 + 25x^2 + 16x - 12 (a) list all the possible rational zeroes (b) find actual rational zeroes (c) find all the zeroes (some zeroes may be complex numbers) (d) write p(x) in completely factored form p(x) = (x - r_1) (x - r_2) (x - r_3) (x - r_4). Find an equation for the polynomial graph on the left below & another equation for the parabola graph on the right below: (a) Find an equation for a circle of radius 20 centered at the origin (b) Calculate the points of intersection of the circle of part (a) with the parabola drawn to the right aboveExplanation / Answer
The equation of circle is (x-h)^2 +(y-k)^2 = r^2
For origin (h,k) = (0,0) and radius =20
Equation is (x-0)^2 +(y-0)^2 =20^2
x2 +y^2 =400
now from graph the points are (10,0) and (0,-30)
now, slope = 3
eqation of parabola is y = 4ax =4 (20)x = 80x.
Substitute, y=80x in equation of circle
x^2 + (80x)^2 =400
x^2 +6400 x^2 =400
6401x^2 =400
x=0.25.
y= 80* 0.25 = 20
Point of intersect ion is (0.25 , 20)