To determine the values of the coefficients and the constant term for the equation [tex]\(0 = 2 + 3x^2 - 5x\)[/tex], let’s rewrite this equation in the general quadratic form:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
Here, [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] represent the coefficients of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant term, respectively. Let's match the terms from our given equation to this standard form:
[tex]\[ 3x^2 - 5x + 2 = 0 \][/tex]
By comparing the given equation with the general form, we can identify the coefficients:
- The coefficient of [tex]\(x^2\)[/tex] (which is [tex]\(a\)[/tex]) is [tex]\(3\)[/tex].
- The coefficient of [tex]\(x\)[/tex] (which is [tex]\(b\)[/tex]) is [tex]\(-5\)[/tex] (note that the sign is included).
- The constant term (which is [tex]\(c\)[/tex]) is [tex]\(2\)[/tex].
So the values are:
[tex]\[
\begin{array}{l}
a = 3 \\
b = -5 \\
c = 2
\end{array}
\][/tex]
