To determine the value of "c" in the quadratic equation [tex]\(3x^2 + 5x + 7 = 0\)[/tex], let's review the structure of a standard quadratic equation.
A quadratic equation is generally given in the form:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
Here,
- [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.
Given the specific quadratic equation:
[tex]\[ 3x^2 + 5x + 7 = 0 \][/tex]
We can identify the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] as follows:
- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(3\)[/tex], so [tex]\(a = 3\)[/tex].
- The coefficient of [tex]\(x\)[/tex] is [tex]\(5\)[/tex], so [tex]\(b = 5\)[/tex].
- The constant term is [tex]\(7\)[/tex], so [tex]\(c = 7\)[/tex].
Therefore, the value of [tex]\(c\)[/tex] in the quadratic equation [tex]\(3x^2 + 5x + 7 = 0\)[/tex] is:
[tex]\[ c = 7 \][/tex]
So, the correct answer from the options provided is:
[tex]\[ 7 \][/tex]
