Identifying the Components of a Quadratic Function

What are the values for the coefficients and constant term of [tex]\(0 = 2 + 3x^2 - 5x\)[/tex]?

[tex]\(a = \_\_\_\_\)[/tex]

[tex]\(b = \_\_\_\_\)[/tex]

[tex]\(c = \_\_\_\_\)[/tex]



Answer :

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]