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Solve the quadratic equation graphically using at least two different approaches. When necessary, give your solutions to the nearest hundredth.

[tex]\[ 18x^2 = 4100 \][/tex]

a. \( x = 11 \) or \( x = -11 \)

b. \( x = 1.12 \) or \( x = 0.82 \)

c. \( x = 5 \) or \( x = 0.5 \)

d. \( x = 1 \) or \( x = -1 \)

Please select the best answer from the choices provided:

A.
B.
C.
D.

Sagot :

GinnyAnsweridn
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]
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