Answer :
To solve the quadratic equation \( 18x^2 = 4100 \) graphically, let's take a step-by-step approach to find the roots and compare them to the provided options:
### Step-by-Step Solution:
1. Given Quadratic Equation:
[tex]\[ 18x^2 = 4100 - 0 \][/tex]
2. Simplify the Equation:
[tex]\[ 18x^2 = 4100 \][/tex]
3. Isolate \( x^2 \):
[tex]\[ x^2 = \frac{4100}{18} \][/tex]
4. Calculate \( \frac{4100}{18} \):
[tex]\[ x^2 = 227.7778 \][/tex]
5. Take the Square Root of Both Sides to Solve for \( x \):
[tex]\[ x = \pm \sqrt{227.7778} \][/tex]
6. Compute the Square Root of 227.7778:
[tex]\[ x \approx \pm 15.09 \][/tex]
### Final Solutions:
[tex]\[ x \approx 15.09 \quad \text{or} \quad x \approx -15.09 \][/tex]
### Comparison with Given Options:
- Option a. \( x = 1 \) or \( x = -1 \) is incorrect.
- Option b. \( x = 1.12 \) or \( x = 0.82 \) is incorrect.
- Option c. \( x = 5 \) or \( x = 0.5 \) is incorrect.
- Option d. \( x = 15.09 \) or \( x = -15.09 \) is the correct option.
Hence, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
### Step-by-Step Solution:
1. Given Quadratic Equation:
[tex]\[ 18x^2 = 4100 - 0 \][/tex]
2. Simplify the Equation:
[tex]\[ 18x^2 = 4100 \][/tex]
3. Isolate \( x^2 \):
[tex]\[ x^2 = \frac{4100}{18} \][/tex]
4. Calculate \( \frac{4100}{18} \):
[tex]\[ x^2 = 227.7778 \][/tex]
5. Take the Square Root of Both Sides to Solve for \( x \):
[tex]\[ x = \pm \sqrt{227.7778} \][/tex]
6. Compute the Square Root of 227.7778:
[tex]\[ x \approx \pm 15.09 \][/tex]
### Final Solutions:
[tex]\[ x \approx 15.09 \quad \text{or} \quad x \approx -15.09 \][/tex]
### Comparison with Given Options:
- Option a. \( x = 1 \) or \( x = -1 \) is incorrect.
- Option b. \( x = 1.12 \) or \( x = 0.82 \) is incorrect.
- Option c. \( x = 5 \) or \( x = 0.5 \) is incorrect.
- Option d. \( x = 15.09 \) or \( x = -15.09 \) is the correct option.
Hence, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
