What you must do for this case is find the cut points with the x axis.
For this, we evaluate when:
y = 0
0 = ax ^ 2 + 10x + 1
We solve the polynomial using the resolver:
x = (- b +/- root (b ^ 2 - 4ac)) / 2a
We see where the root is defined:
b ^ 2 - 4ac> = 0
10 ^ 2 - 4 * a * 1> = 0
100> = 4 * a * 1
100/4> = a
25> = a
We go where the denominator is not defined:
2a = 0
a = 0
Therefore the values of a must be between 0 and 25, written mathematically:
a = (0, 25]
answer:
a = (0, 25]
