To answer the question, let's carefully transform each given equation into its standard form and then identify if they are quadratic equations. A quadratic equation generally has the standard form [tex]\( ax^2 + bx + c = 0 \)[/tex]. We will also find the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] for each equation.
### Equation 1: [tex]\( 5x^2 = 0 \)[/tex]
1. Rewrite the equation in standard form:
[tex]\[ 5x^2 + 0x + 0 = 0 \][/tex]
2. Identify the coefficients:
[tex]\[ a = 5, \, b = 0, \, c = 0 \][/tex]
### Equation 2: [tex]\( 7h(2h - 3) = 0 \)[/tex]
1. Expand and rewrite the equation:
[tex]\[ 7h(2h - 3) = 0 \Rightarrow 14h^2 - 21h = 0 \][/tex]
2. Rewrite in standard form:
[tex]\[ 14h^2 - 21h + 0 = 0 \][/tex]
3. Identify the coefficients:
[tex]\[ a = 14, \, b = -21, \, c = 0 \][/tex]
### Equation 3: [tex]\( c(2c - 3) = 0 \)[/tex]
1. Expand and rewrite the equation:
[tex]\[ c(2c - 3) = 0 \Rightarrow 2c^2 - 3c = 0 \][/tex]
2. Rewrite in standard form:
[tex]\[ 2c^2 - 3c + 0 = 0 \][/tex]
3. Identify the coefficients:
[tex]\[ a = 2, \, b = -3, \, c = 0 \][/tex]
### Equation 4: [tex]\( 2f(11f - 3) = 0 \)[/tex]
1. Expand and rewrite the equation:
[tex]\[ 2f(11f - 3) = 0 \Rightarrow 22f^2 - 6f = 0 \][/tex]
2. Rewrite in standard form:
[tex]\[ 22f^2 - 6f + 0 = 0 \][/tex]
3. Identify the coefficients:
[tex]\[ a = 22, \, b = -6, \, c = 0 \][/tex]
### Equation 5: [tex]\( (x - 3)(x + 6) = 0 \)[/tex]
1. Expand and rewrite the equation:
[tex]\[ (x - 3)(x + 6) = 0 \Rightarrow x^2 + 6x - 3x - 18 = 0 \Rightarrow x^2 + 3x - 18 = 0 \][/tex]
2. Rewrite in standard form:
[tex]\[ x^2 + 3x - 18 = 0 \][/tex]
3. Identify the coefficients:
[tex]\[ a = 1, \, b = 3, \, c = -18 \][/tex]
Now, let's summarize the results in the table format:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Standard Form} & a, b, c \\
\hline
1. & 5x^2 + 0x + 0 = 0 \quad (5, 0, 0) \\
\hline
2. & 14h^2 - 21h + 0 = 0 \quad (14, -21, 0) \\
\hline
3. & 2c^2 - 3c + 0 = 0 \quad (2, -3, 0) \\
\hline
4. & 22f^2 - 6f + 0 = 0 \quad (22, -6, 0) \\
\hline
5. & x^2 + 3x - 18 = 0 \quad (1, 3, -18) \\
\hline
\end{array}
\][/tex]
From the analysis, all the given equations are quadratic equations, and their coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] have been identified for each equation.
