Goal
Given a polynomial y = ax² + bx + c, calculate :
- the roots (intersections with the X axis), if existing (there can be 0, 1 or 2),
- the only intersection with the Y axis (always existant in our situation).
Output those points, from left-most to right-most.
To get the root(s) abscissa(s), first calculate delta = b² - 4·a·c.
If delta < 0, there are no roots (our graph will remain strictly above or below the X axis);
If delta = 0, there is a unique root (that is also the minimum or maximum of the function);
If delta > 0, there are 2 roots.
Then, the root abscissas are given by the formula : [x1, x2] = (-b ± sqrt(delta)) / (2·a).
Be aware that...
If a = 0, we obtain a straight line, crossing the X axis in (-c / b, 0).
If a = 0 and b = 0, we have a horizontal line y = c.
In the special case a, b, c = 0, we have y = 0 and the only point to output will be (0,0).
Examples :
y = 1x² + 0x + 1 (= x² + 1)
Input : 1 0 1
Output : (0,1)
y = 1x² + 0x - 1 (= x² - 1)
Input : 1 0 -1
Output : (-1,0),(0,-1),(1,0)
Input
Line 1 : 3 decimal numbers a, b, c, representing the polynomial coefficients.
Output
Line 1 : a comma-separated list of
P points (intersections with the X & Y axis), ordered from left to right, with each point formatted as
(x,y) without spaces.
Every x and y coordinate,
at display time, must be rounded to
maximum 2 decimals (only the meaningful ones) :
5.000 => 5
1.2001 => 1.2
0.1256 => 0.13
Constraints
-100 < a < 100
-100 < b < 100
-100 < c < 100
1 ≤ P ≤ 3
