To find the coefficients and the constant term of the quadratic equation [tex]\(0=2+3x^2-5x\)[/tex], we need to compare it to the standard form of a quadratic equation, which is [tex]\(ax^2 + bx + c = 0\)[/tex].
### Step-by-Step Solution
1. Identify the term corresponding to [tex]\(a\)[/tex]:
- The term involving [tex]\(x^2\)[/tex] in the equation is [tex]\(3x^2\)[/tex]. Therefore, the coefficient [tex]\(a = 3\)[/tex].
2. Identify the term corresponding to [tex]\(b\)[/tex]:
- The term involving [tex]\(x\)[/tex] in the equation is [tex]\(-5x\)[/tex]. Therefore, the coefficient [tex]\(b = -5\)[/tex].
3. Identify the constant term [tex]\(c\)[/tex]:
- The constant term in the equation is [tex]\(2\)[/tex]. Therefore, [tex]\(c = 2\)[/tex].
Summarizing these values, we have:
[tex]\[a = 3\][/tex]
[tex]\[b = -5\][/tex]
[tex]\[c = 2\][/tex]
So, the coefficients and constant term for the equation [tex]\(0 = 2 + 3x^2 - 5x\)[/tex] are:
[tex]\[
\begin{aligned}
&a = 3 \\
&b = -5 \\
&c = 2
\end{aligned}
\][/tex]
