Certainly! Let's go through each of your equations, rewrite them into standard form, and identify the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
### Question 2
Starting with:
[tex]\[ x^2 - 64 = 0 \][/tex]
This equation is already in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex].
Identifying coefficients:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 0\)[/tex]
- [tex]\(c = -64\)[/tex]
### Question 4
Next, consider:
[tex]\[ 6x(x + 1) = 0 \][/tex]
First, distribute the [tex]\(6x\)[/tex]:
[tex]\[ 6x^2 + 6x = 0 \][/tex]
This is now in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex].
Identifying coefficients:
- [tex]\(a = 6\)[/tex]
- [tex]\(b = 6\)[/tex]
- [tex]\(c = 0\)[/tex]
### Question 5
Next equation:
[tex]\[ 4x^2 = 3x + 10 \][/tex]
First, move all terms to one side to get it into standard form:
[tex]\[ 4x^2 - 3x - 10 = 0 \][/tex]
Identifying coefficients:
- [tex]\(a = 4\)[/tex]
- [tex]\(b = -3\)[/tex]
- [tex]\(c = -10\)[/tex]
### Question 8
Starting from:
[tex]\[ (x + 3)(x - 3) = x(4x + 5) \][/tex]
Expand both sides:
[tex]\[ x^2 - 9 = 4x^2 + 5x \][/tex]
Move all terms to one side to get it into standard form:
[tex]\[ x^2 - 4x^2 - 5x - 9 = 0 \][/tex]
[tex]\[ -3x^2 - 5x + 9 = 0 \][/tex]
Identifying coefficients:
- [tex]\(a = -3\)[/tex]
- [tex]\(b = -5\)[/tex]
- [tex]\(c = 9\)[/tex]
### Question 10
Lastly:
[tex]\[ x(2x - 4) = (x - 2)^2 \][/tex]
Expand both sides:
[tex]\[ 2x^2 - 4x = x^2 - 4x + 4 \][/tex]
Move all terms to one side to get it into standard form:
[tex]\[ 2x^2 - 4x - x^2 + 4x - 4 = 0 \][/tex]
[tex]\[ x^2 - 4 = 0 \][/tex]
After simplification we can rewrite it as:
[tex]\[ x^2 = 4 \][/tex]
[tex]\[ x^2 - 4 = 0 \][/tex]
Identifying coefficients:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 0\)[/tex]
- [tex]\(c = 0\)[/tex]
### Summary
After rewriting each quadratic equation in standard form, we have identified the following coefficients:
1. [tex]\(x^2 - 64 = 0\)[/tex] [tex]\(\Rightarrow a = 1, b = 0, c = -64\)[/tex]
2. [tex]\(6x(x + 1) = 0\)[/tex] [tex]\(\Rightarrow a = 6, b = 6, c = 0\)[/tex]
3. [tex]\(4x^2 = 3x + 10\)[/tex] [tex]\(\Rightarrow a = 4, b = -3, c = -10\)[/tex]
4. [tex]\((x + 3)(x - 3) = x(4x + 5)\)[/tex] [tex]\(\Rightarrow a = -3, b = -5, c = 9\)[/tex]
5. [tex]\(x(2x - 4) = (x - 2)^2\)[/tex] [tex]\(\Rightarrow a = 1, b = 0, c = 0\)[/tex]
These steps guide you through converting the given quadratic expressions to their standard form and identifying the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] for each equation.
