To determine the discriminant of the polynomial [tex]\(4x^2 + 4x + 1\)[/tex], we use the discriminant formula for a quadratic equation of the form [tex]\(ax^2 + bx + c\)[/tex]:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
In this equation:
- [tex]\(a\)[/tex] is the coefficient of [tex]\(x^2\)[/tex],
- [tex]\(b\)[/tex] is the coefficient of [tex]\(x\)[/tex],
- [tex]\(c\)[/tex] is the constant term.
For the given polynomial [tex]\(4x^2 + 4x + 1\)[/tex]:
- [tex]\(a = 4\)[/tex]
- [tex]\(b = 4\)[/tex]
- [tex]\(c = 1\)[/tex]
Now, substitute these values into the discriminant formula:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
[tex]\[ \Delta = 4^2 - 4 \cdot 4 \cdot 1 \][/tex]
[tex]\[ \Delta = 16 - 16 \][/tex]
[tex]\[ \Delta = 0 \][/tex]
The discriminant of the polynomial [tex]\(4x^2 + 4x + 1\)[/tex] is [tex]\(\Delta = 0\)[/tex].
Therefore, the correct choice is:
C. 0
