The discriminant is calculated using the formula:
[tex]D={b}^{2}-4ac[/tex]
First, find a, b and c
The standard form of a quadratic function is:
[tex]f(x) = {ax}^{2} + bx + c[/tex]
So if we look at the formula we get:
[tex]a = 1[/tex]
[tex]b = - 2[/tex]
[tex]c = 5[/tex]
Then, insert them into the formula:
[tex]( { - 2}^{2} ) - 4 \times 1\times 5[/tex]
[tex]D=4-20[/tex]
So the dicriminant is:
D = -16
Meaning that the graph of the function has no roots (zeroes).
